Math 8 Substitution Method Review

Multiple Choice

What does a "solution to a system of equations" mean?

• It's the point where both equations equal zero

• It's the point where graphs of both equations cross the y-axis

• It's the point that is true for both equations at the same time

• It's the point where graphs of both equations cross the x-axis

Multiple Choice

Substitution method is a good method when at least one of the equations has:

• a variable isolated ( x = or y = )

• both written in standard form

• no decimals

Multiple Choice

What does it mean to substitute?

• to add different variables together and see what you get

• to graph and find the intersection

• guess and check

• to replace the value of a variable with an equivalent expression

Steps For Solving By Substitution

Step 1: Pick an equation

Step 2: ​When solving a system with 2 equations. Pick 1 equation and get x OR y by itself.

x=___ or y=____​

​Step 3: Substitute x =___ or y = ___ from the first step into the other equation and solve for the variable.

Step 4: Substitute your answer into one of the original equations and solve for the other variable.

Multiple Choice

Which of the following correctly shows substituting the first equation into the second equation?

• x + 3x = -32

• y + y = -32

• y = 3(x + y = -32)

• 3y + y = -32

Multiple Choice

Which of the following correctly shows substituting the first equation into the second equation?

• y = 9(2x + 10) - 2

• 9x - 2 = 3x + 10

Multiple Choice

Which of the following correctly shows substituting the first equation into the second equation?

• 5x = -x + 4

• 5(y + 4) + 6y = 13

• 5x + 6(-x + 4) = 13

• 5x + (-x + 4) = 13

Multiple Choice

Which of answer shows the correct steps to solve for x?

• -3x + 4(3x - 5) = 7

  -3x + 12x - 5 = 7

  9x - 5 = 7
  9x = 12
  x = 1.25

• -3x + 4(3x - 5) = 7

  -3x + 12x - 20 = 7

  9x - 20 = 7

  9x = 27

  x = 3

• -3x + 4(3x - 5) = 7

  -3x + 12x - 15 = 7

  9x - 15 = 7
  9x = 9
  x = 1

​x = 4 + 2y

2(4+2y) + y = 8

8 + 4y +y = 8
8 + 5y = 8
5y = 0
y = 0

x = 4 + 2(0)
x = 4
(4, 0)

2(4) + 0 = 8
8 + 0 = 8
TRUE

Math Response

Rewrite the 2nd equation substituting the expression from the first equation in for y:

$$y=2x+7$$

$$3x+2y=7$$

Type answer here

Correct Answer: 3x+2\left(2x+7\right)=7

Deg^°

Rad

Math Response

Rewrite the second equation by substituting for x:
$$x=3y+4$$
$$2x+4y\ =\ 15$$

Type answer here

Correct Answer: 2\left(3y+4\right)+4y=15

Deg^°

Rad

Math Response

Write an equation that can be created by substitution:
$$x=2y+8$$
$$x=5y+2$$

Type answer here

Correct Answer: 2y+8=5y+2

Deg^°

Rad

Multiple Choice

(SCRAP PAPER) Solve the system by substitution:

y = 3x + 1

y = -3x + 7  

• (1, 4)

• (2, 1)

• (0, 1)

• (3, -2)

• (6, 7)

Multiple Choice

(SCRAP PAPER) Solve the system by substitution:

y = 2x + 7

2x + y = -1

• (-2, 3)

• (1, -3)

• (5, 17)

• (2, -5)

• (-1, 1)

Multiple Choice

(SCRAP PAPER) Solve the system by substitution:

y = -3x - 1

x + 3y = 13 

• (-2, 5)

• (13, 0)

• (1, 4)

• (-1, 2)

• (7, 2)

Multiple Choice

(SCRAP PAPER) Solve the system by substitution:
4x - 2y = 2

x = y - 1 

• (2, 3)

• (5, 6)

• (1, 0)

• (-1, -2)

• (-2, -5)

Steps For Solving By Substitution

Step 1: Solve 1 equation for 1 of the variables.

x=___ or y=____​

​

Step 2:​ Substitute x =___ or y = ___ from the first step into the other equation and solve for the variable.

​

​Step 3: Substitute your answer into one of the original equations and solve for the other variable.

​

Step 4: Write your answer as an ordered pair.​

​

Multiple Choice

Which answer has a correct first step for this system:

3x + 3y = 3

y = 3x + 5

• The variable is already isolated, so we've already solved the system.

• The variable is already isolated for y, so we substitute it in the first equation and solve for x

  3x + 3(3x + 5) = 3

• The variable is already isolated for y, so we substitute it in the second equation and solve for x

  y = 3(3x + 3y) = 3

Multiple Choice

What is the best choice for solving the given system?

y= 4x-1

y= 2x-5

• Solve both equations for x.

• Plug in 4x-1 for y in the second equation.

• Plug in 4x-1 for x in the second equation.

• Plug in 2x-5 for x in the first equation.

Multiple Choice

Rob is solving the system shown. What is the solution?

• (-1, 3)

• (3, -1)

• There is no solution.

• There are infinitely many solutions.

Fill in the Blanks

(Scrap Paper) Find the solution to this system of equations using substitution:

x + 2y = 0 and x = 2y - 1

*Enter your solution as an ordered pair (x,y)

Fill in the Blanks

Find the solution to this system using substitution:

3x + y = -1 and y = 3x + 5

*Enter your solution as an ordered pair (x,y)

​​If you still do not understand, watch the video.

​​If you need more practice, click the link:
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-with-substitution/e/systems_of_equations_with_substitution