1. Solving Systems by Substitution
Lesson 25
Linear Equations
Solving Systems by Substitution

2. Warm-Up Solve each equation for x. 3x + 4x – 7 = 21 10 + 2x – 4x = 12

3. Solving Systems by Substitution
Target:
Determine the solution to a system of equations
using the substitution method.

4. Vocabulary
Substitution Method: A method for solving a system of equations.

5. Solving Systems of Linear Equations by Substitution
Solve one of the linear equations for a variable (isolate x or y), if necessary.
Replace the variable in the second equation with the expression that you solved for in Step 1. Solve for the variable in your new equation.
Substitute your solution into the equation from Step 1 to find the value of the other variable. State your full answer as an ordered pair (x, y).
Verify that the ordered pair is the solution by substituting the x- and y-values into both equations in the system or by graphing the system to confirm that the point of intersection matches your solution.

6. Example 1 y = –2(3) + 5 y = –6 + 5 y = –1 Solution: (3, –1)
Use the substitution method to solve the system of linear equations. y = –2x + 5 4x + 3y = 9 4x + 3(–2x + 5) = 9 4x – 6x + 15 = 9 –2x + 15 = 9 – 15 – 15 –2x = –6 –2 –2 x = 3
y = –2(3) + 5
y = –6 + 5
y = –1
Solution: (3, –1)

8. Exit Problems Solve the system of equations using the substitution
method.
x = 4y – 5
2x + 3y = 23

9. Communication Prompt Why do you think there are multiple methods in
mathematics to find the answer to a problem?