Solving Systems of Equations by the Substitution Method

Quick Review of the Graphing Method:

How many solutions does the graph have?

• One solution

• No solution

• Infinite solutions

Quick Review of the Graphing Method:

How many solutions does the graph have?

• One solution

• No solution

• Infinite solutions

Quick Review of the Graphing Method:

How many solutions does the graph have?

• One solution

• No solution

• Infinite solutions

The first step in solving a system of equations using the SUBSTITUTION METHOD is __________.

(Read all the answers before choosing one.)

• get x by itself

• get y by itself

• get EITHER x or y by itself

• add the equations together

Which answer has a correct next step for this system? (Read all three answers carefully before selecting one!)

y = 6x

2x + 5y = 32

• 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 second equation like this:

  2(6x) + 5y = 32

• The variable is already isolated for y, so we substitute it in the second equation like this:

  2x + 5(6x) = 32

Use the system of equations below to answer the question.

After substituting the first equation into the second one and working it out, I got x = 1. What should I do next?

y = 6x

2x + 5y = 32

• Fill in 1 for x in y = 6x

• Fill in 1 for y in y = 6x

• Fill in 1 for y in 2x + 5y = 32

Which answer has a correct next step for this system? (Read all three answers carefully before selecting one!)

3x + 4y = 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 3x + 5 in the first equation like this:

  3x + 4(3x + 5) = 3

• The variable is already isolated for y, so we substitute 3x + 5 in the second equation like this:

  3(3x + 5) + 4y = 3

What is the solution to this system?

(Use the substitution method.)

8x - 2y = 6

y = 3x

• (3, 9)

• (5, 2)

• (2, 3)

• (3, 2)

Solve the system of equations by using the Substitution Method.

y = 2x - 4

7x - 2y = 5

• (-1, -6)

• (-1, -8)

• (-2, 6)

• (1, -8),