Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (2024)

Table of Contents
All Common Core: 8th Grade Math Resources Example Questions Example Question #1 : How To Find The Solution For A System Of Equations Example Question #2 : How To Find The Solution For A System Of Equations Example Question #1 : How To Find The Solution For A System Of Equations Example Question #2 : How To Find The Solution For A System Of Equations Example Question #3 : How To Find The Solution For A System Of Equations Example Question #4 : How To Find The Solution For A System Of Equations Example Question #1 : How To Find The Solution For A System Of Equations Example Question #1 : Solve Systems Of Two Linear Equations: Ccss.Math.Content.8.Ee.C.8b Example Question #281 : Equations / Inequalities Example Question #51 : How To Find The Solution For A System Of Equations All Common Core: 8th Grade Math Resources References

All Common Core: 8th Grade Math Resources

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Example Questions

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Common Core: 8th Grade Math Help » » Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b

Example Question #1 : How To Find The Solution For A System Of Equations

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (1)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (2)

Solve the system for Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (3)and Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (4).

Possible Answers:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (5)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (6)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (7)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (8)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (9)

Correct answer:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (10)

Explanation:

The most simple method for solving systems of equations is to transform one of the equations so it allows for the canceling out of a variable. In this case, we can multiply Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (11)by Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (12)to get Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (13).

Then, we can add Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (14) to this equation to yield Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (15), so Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (16).

We can plug that value into either of the original equations; for example, Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (17).

So, Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (18)as well.

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Example Question #2 : How To Find The Solution For A System Of Equations

What is the solution to the following system of equations:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (19)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (20)

Possible Answers:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (21)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (22)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (23)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (24)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (25)

Correct answer:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (26)

Explanation:

By solving one equation for Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (27), and replacingSolve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (28) in the other equation with that expression, you generate an equation of only 1 variable which can be readily solved.

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Example Question #1 : How To Find The Solution For A System Of Equations

Solve this system of equations forSolve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (29):

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (30)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (31)

Possible Answers:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (32)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (33)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (34)

None of the other choices are correct.

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (35)

Correct answer:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (36)

Explanation:

Multiply the bottom equation by 5, then add to the top equation:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (37)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (38)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (39)

See Also
8.EE.C.8 Worksheets - Common Core MathCommon Core for High School - Algebra (lessons, worksheets, solutions, examples, games)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (40)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (41)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (42)

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Example Question #2 : How To Find The Solution For A System Of Equations

Solve this system of equations forSolve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (43):

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (44)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (45)

Possible Answers:

None of the other choices are correct.

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (46)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (47)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (48)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (49)

Correct answer:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (50)

Explanation:

Multiply the top equation bySolve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (51):

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (52)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (53)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (54)

Now add:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (55)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (56)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (57)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (58)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (59)

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Example Question #3 : How To Find The Solution For A System Of Equations

Solve this system of equations for Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (60):

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (61)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (62)

Possible Answers:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (63)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (64)

None of the other choices are correct.

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (65)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (66)

Correct answer:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (67)

Explanation:

Multiply the top equation by Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (68):

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (69)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (70)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (71)

Now add:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (72)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (73)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (74)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (75)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (76)

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Example Question #4 : How To Find The Solution For A System Of Equations

Find the solution to the following system of equations.

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (77)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (78)

Possible Answers:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (79)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (80)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (81)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (82)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (83)

Correct answer:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (84)

Explanation:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (85)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (86)

To solve this system of equations, use substitution. First, convert the second equation to isolate Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (87).

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (88)

Then, substituteSolve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (89) into the first equation for Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (90).

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (91)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (92)

Combine terms and solve for Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (93).

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (94)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (95)

Now that we know the value of Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (96), we can solve for Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (97) using our previous substitution equation.

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (98)

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Example Question #1 : How To Find The Solution For A System Of Equations

Find a solution for the following system of equations:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (99)

Possible Answers:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (100)

no solution

infinitely many solutions

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (101)

Correct answer:

no solution

Explanation:

When we add the two equations, theSolve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (102) andSolve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (103) variables cancel leaving us with:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (104) which means there is no solution for this system.

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Example Question #1 : Solve Systems Of Two Linear Equations: Ccss.Math.Content.8.Ee.C.8b

Solve the set of equations:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (105)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (106)

Possible Answers:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (107)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (108)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (109)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (110)

Correct answer:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (111)

Explanation:

Solve the first equation for Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (112):

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (113)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (114)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (115)

Substitute into the second equation:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (116)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (117)

Multiply the entire equation by 2 to eliminate the fraction:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (118)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (119)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (120)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (121)

Using the value of Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (122), solve for Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (123):

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (124)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (125)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (126)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (127)

Therefore, the solution is Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (128)

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Example Question #281 : Equations / Inequalities

Solve the following system of equations:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (129)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (130)

Possible Answers:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (131)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (132)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (133)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (134)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (135)

Correct answer:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (136)

Explanation:

Set the two equations equal to one another:

2x - 2 = 3x + 6

Solve for x:

x = -8

Plug this value of x into either equation to solve for y. We'll use the top equation, but either will work.

y = 2 * (-8) - 2

y = -18

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Example Question #51 : How To Find The Solution For A System Of Equations

Solve this system of equations for Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (137):

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (138)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (139)

Possible Answers:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (140)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (141)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (142)

None of the other choices are correct.

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (143)

Correct answer:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (144)

Explanation:

Multiply the bottom equation by Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (145), then add to the top equation:

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (146)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (147)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (148)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (149)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (150)

Divide both sides bySolve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (151)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (152)

Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (153)

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Solve Systems of Two Linear Equations: CCSS.Math.Content.8.EE.C.8b - Common Core: 8th Grade Math (2024)

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