Solve the following by substitution:

2x - 13 = -4x + 29 6x - 13 = 29 6x = 42 x = 7 y = 2(7) - 13 y = 14 - 13 y = 1 (7, 1)

2x - 13 = -4x + 29 6x - 13 = 29 6x = 42 x = 7 y = 2(7) - 13 y = 14 - 13 y = 1 (1, 7)

2x - 13 = -4x + 29 -2x - 13 = 29 -2x = 42 x = -21 y = 2(-21) - 13 y = -42 - 13 y = -55 (-21, -55)

2x - 13 = -4x + 29 -2x - 13 = 29 -2x = 14 x = -7 y = 2(-7) - 13 y = -14 - 13 y = -27 (-7, -27)

Solve the following by substitution:

2x - (6x + 14) = 2 2x - 6x - 14 = 2 -4x - 14 = 2 -4x = 16 x = -4 y = 6(-4) + 14 y = -24 + 14 y = -10 (-4, -10)

2x - (6x + 14) = 2 2x - 6x + 14 = 2 -4x + 14 = 2 -4x = -12 x = 3 y = 6(3) + 14 y = 18 + 14 y = 32 (3, 32)

2x - (6x + 14) = 2 2x - 6x - 14 = 2 -4x - 14 = 2 -4x = 16 x = -4 y = 6(-4) + 14 y = -24 + 14 y = -10 (-10, -4)

2x - (6x + 14) = 2 2x + 6x + 14 = 2 8x + 14 = 2 8x = -12 x = -1.5 y = 6(-1.5) + 14 y = -9 + 14 y = 5 (-1.5, 5)

Solve the following by substitution:

9x - 2(-7x + 4) = 15 9x + 14x - 8 = 15 23x = 23 x = 1 7(1) + y = 4 7 + y = 4 y = -3 (1, -3)

9x - 2(-7x + 4) = 15 9x - 14x + 4 = 15 -5x = 10 x = -2 7(-2) + y = 4 -14 + y = 4 y = 18 (-2, 18)

9x - 2(-7x + 4) = 15 9x + 14x + 4 = 15 5x = 20 x = 4 7(4) + y = 4 28 + y = 4 y = -24 (4, -24)

9x - 2(-7x + 4) = 15 9x - 14x + 8 = 15 -5x = 7 x = -1.4 7(-1.4) + y = 4 -9.8 + y = 4 y = 13.8 (-1.4, 13.8)

Solve the following by substitution:

9(2y - 15) + 7y = -10 18y - 135 + 7y = -10 25y - 135 = -10 25y = 125 y = 5 x - 2(5) = -15 x - 10 = -15 x = -5 (-5, 5)

9(2y - 15) + 7y = -10 18y - 15 + 7y = -10 25y - 15 = -10 25y = -25 y = -1 x - 2(-1) = -15 x + 2 = -15 x = -13 (-1, -13)

9(2y - 15) + 7y = -10 18y - 135 + 7y = -10 25y - 135 = -10 25y = -125 y = -5 x - 2(-5) = -15 x + 10 = -15 x = -25 (-5, -25)

9(2y - 15) + 7y = -10 18y - 135 + 7y = -10 25y - 135 = -10 25y = 125 y = 5 x - 2(5) = -15 x + 10 = -15 x = -25 (-5, -25)

Solve the following by elimination:

0 = 11x + 22 -22 = 11x x = -2 y = 5(-2) + 17 y = -10 + 17 y = 7 (-2, 7)

0 = 11x + 22 22 = 11x x = 2 y = 5(2) + 17 y = 10 + 17 y = 27 (2, 27)

0 = -1x + 22 -22 = -1x x = 22 y = 5(22) + 17 y = 110 + 17 y = 117 (22, 117)

0 = -1x + 22 22 = -1x x = -22 y = 5(-22) + 17 y = -110 + 17 y = -93 (-22, -93)

Solve the following by elimination:

0x - 4y = 16 -4y = 16 y = -4 2x + (-4) = -16 2x - 4 = -16 2x = -12 x = -6 (-6, -4)

0x - 4y = 16 -4y = 16 y = -4 2x + (-4) = -16 2x + 4 = -16 2x = -20 x = -10 (-10, -4)

0x - 4y = 16 4y = 16 y = 4 2x + (4) = -16 2x + 4 = -16 2x = -20 x = -10 (-10, 4)

0x - 4y = 16 -4y = 16 y = 4 2x + (4) = -16 2x - 4 = -16 2x = -12 x = -6 (-6, 4)

Solve the following by elimination:

-4x + 0y = 36 -4x = 36 x = -9 (-9) - 3y = -12 -3y = -3 y = 1 (-9, 1)

-4x + 0y = 36 -4x = 36 x = -9 (-9) - 3y = -12 -3y = -21 y = 7 (-9, 7)

-4x + 0y = 36 4x = 36 x = 9 (9) - 3y = -12 -3y = -21 y = 7 (9, 7)

-4x + 0y = 36 4x = 36 x = 9 (9) - 3y = -12 -3y = -3 y = 1 (9, 1)

Solve the following by elimination:

8x + 2y = 14 -8x - 2y = -14 0x + 0y = 0 0 = 0 Infinitely Many Solutions

8x + 2y = 14 -8x - 2y = -14 0x + 0y = 0 0 = 0 No Solution

8x + 2y = 14 8x - 2y = 14 16x + 0y = 24 x = 1.5 4(1.5) + y = 7 6 + y = 7 y = 1 (1.5, 1)

8x + 2y = 14 -8x - 2y = -14 0x + 0y = 0 y = 0 4x + 0 = 7 x = 1.75 (1.75, 0)

The sum of two numbers is 71. If their difference is 37, find both numbers. What are the variables and the systems?

Variables: let x = 1st # let y = 2nd # Systems: x + y = 71 x - y = 37

Variables: let x = 1st # let y = 2nd # Systems: x - y = 71 x + y = 37

The florist charges $31.75 for eight roses and five carnations. For one rose and three carnations, it costs $5.75. What is the cost for a carnation? What are the variables and the systems?

Variables: let x = roses let y = carnations Systems: 8x + 5y = 31.75 x + 3y = 5.75

Variables: let x = roses let y = carnations Systems: 5x + 8y = 31.75 3x + y = 5.75

Mitch bought a total of 13 pizzas and buckets of wings for his big Super Bowl party. If it costs $11.75 for a pizza and $19.95 for a bucket of wings and he spent $193.75, how many buckets of wings did he buy? What are the variables and systems?

Variables: let x = Pizza let y = Buckets of Wings Systems: x + y = 13 11.75x + 19.95y = 193.75

Variables: let x = Pizza let y = Buckets of Wings Systems: 11.75x + 19.95y = 13 x + y = 193.75

A total of 800 pre-sale tickets and tickets at the gate were sold to the football city championship game. If the number of tickets sold at the gate was thirteen less than twice the number of pre-sale tickets, how many pre-sale tickets were sold? What are the variables and sytems?

Variables: let x = pre-sale tickets let y = tickets sold at gate Systems: x + y = 800 y = 2x - 13

Variables: let x = pre-sale tickets let y = tickets sold at gate Systems: x + y = 800 2x +y = 13

Unit 5 Study Guide Review: Systems of Equations

Authored by Kathryn Ebert

Mathematics

8th Grade

CCSS covered

Used 6+ times

Unit 5 Study Guide Review: Systems of Equations

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which are the types of Solutions Possible for a system of equations?

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What are the two equations for the following graph?

y=x-1

y=-2x-3

y=x-1

y=-1/2x-3

y=-x-1

y=-2x-3

y=-x-1

y=-1/2x-3

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the solution to this graph?

One Solution:

(4,-5)

Infinite Solution

No Solution

One Solution:

(-5,4)

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What are the equations in the graph?

y=3x+7

y=-3x+7

y=3x-7

y=-3x+7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the solution to this graph?

one solution

infinite solutions

no solution

one solution

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve the following by graphing (match with the correct Graph and Solution):

Tags

CCSS.8.EE.C.8B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve the following by graphing (match with the correct Graph and Solution):

Tags

CCSS.8.EE.C.8B

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