Substitution Method

Substitution Method

​A system of equations is two or more equations with the same variables.

​

​

​

​One method to solve a system of equations is called the substitution method.

​Since y = x - 4, we can substitute x - 4 into the other equation for y.

​

​Then it is easy to solve for x. Once you have the x value of 7, substitute that into either original equation to solve for y. The final answer is x = 7 and y = 3.

​Example

Multiple Choice

Which equation is correctly using substitution for the system shown?

y = x + 6

y = -2x − 3

• x + 6 = -2x − 3

• y = x + 6 − 2x − 3

Multiple Choice

Solve using Substitution

• (3,8)
• (8,3)
• (0,2)
• (2,0)

Multiple Choice

Solve the system by substitution.

y = 2x − 11

2x − 8y = 4

• (6, 1)

• (6, −4)

• (6, −1)

• Infinite number of solutions

• No Solution

Multiple Choice

Solve:

x = -3y - 17

2x + 3y = -7

• (1, -2)

• (3, 0)

• (-5, -2)

• (10 , -9)

• (10, 2)

Multiple Choice

Solve the system of equations using substitution:

4x - 2y = 6

y = 3x - 3

• (3, 6)

• (0, 1)

• (0, -3)

• (2, 3)

• No solution

Multiple Choice

What is the solution to the system of equations?

y = 3x - 8

y = 4 - x

• (3, 1)

• (1, 3)

• (-3, 1)

• (3, -1)

Multiple Choice

Solve the system of equations by substitution.
y = -4x + 5
y =  3x - 16

• (-3, -25)
• (3,-7)
• (11, 17)
• (21, 47)

Multiple Choice

Determine if the system has one solution, infinitely many solutions, or no solution after using the substitution method.  

• One Solution
• Infinitely Many Solutions
• No Solution