Lesson 26 Linear Equations Solving Systems Using Elimination

Lesson 26 Linear Equations Solving Systems Using Elimination

Warm-Up Solve each equation for y given the x-value. 1. 5 x + 4 y = 22 when x = 2 2. x – 8 y = – 3 when x = 5 3. – 2 x + 9 y = – 30 when x = – 3

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

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.

Solving Systems of Linear Equations by Elimination 1. 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. 2. Multiply one or both equations so that one of the variables (x or y) have coefficients that are opposites. 3. Add the columns together. One variable should cancel out by adding to zero. Solve for the remaining variable. 4. Substitute your solution into either of the original equations and solve for the other variable. 5. 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.

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

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

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

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

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?