1. Solving Systems Using Elimination
Lesson 26
Linear Equations
Solving Systems Using Elimination

2. Warm-Up Solve each equation for y given the x-value.
5x + 4y = 22 when x = 2
x – 8y = –3 when x = 5
–2x + 9y = –30 when x = –3

3. Solving Systems Using Elimination
Target:
Determine the solution to a system of equations
using the elimination method.

4. Vocabulary
Elimination Method: A method for solving a system of equations that involves combining two equations in a way that will “eliminate” one of the variables.

5. Solving Systems of Linear Equations by Elimination
Arrange the equations so the common variables are lined up vertically in columns and the constants are alone on one side of the equals sign.
Multiply one or both equations so that one of the variables (x or y) have coefficients that are opposites.
Add the columns together. One variable should cancel out by adding to zero. Solve for the remaining variable.
Substitute your solution into either of the original equations and solve for the other variable.
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
Use the elimination method to solve the system of linear equations. 3x – 2y = 1 2x + 2y = 4 5x = x = 1
2(1) + 2y = 4
2 + 2y = 4
– – 2
2y = 2
y = 1
Solution: (1, 1)

7. Example 2 Use the elimination method to solve the system of linear
equations.
3x + y = 7
2x + 5y = 22
Multiply first equation by –5 to get opposites on the y variable:
–5(3x + y = 7) → –15x – 5y = –35

8. Example 2 (continued)
Use the elimination method to solve the system of linear equations. –15x – 5y = –35 2x + 5y = 22 –13x = –13 –13 –13 x = 1
Original equation:
3x + y = 7
3(1) + y = 7
3 + y = 7
– – 3
y = 4
Solution: (1, 4)

9. Exit Problems Use the elimination method to solve the system of
linear equations.
–3x – y = –4
5x + 2y = 12

10. Communication Prompt You have learned four ways for solving systems of
equations: graphing, tables, substitution and elimination.
Which method do you like best and why?