3-3: Solving Linear Systems by Linear Combination

Goal: Solve a system of linear equations in two variables by the linear combination

method

Warm Up ExercisesSolve the system by substitution:

y = -2x x + y = 4-3x – y = 1 -2x+ 3y = 7

Using the Linear Combination MethodStep 1: Multiply, if necessary, one or both

equations by a constant so that the coefficients of one of the variables differ only in sign.

Step 2: Add the revised equations from step 1. Combining like terms will eliminate one variable. Solve for the remaining variable.

Step 3: Substitute the value obtained in Step 2 into either of the original equations and solve for the other variable.

Step 4: Check the solution in each of the original equations.

Solve the linear system using the linear combination method:

3x + y = 1 x + 2y = 2-3x + y = 7 x – 2y = 6

Solve the linear system using the linear combination method:

2x – 3y = 6 8x + 2y = 44x – 5y = 8 -2x + 3y = 13

Solve the linear system using the linear combination method:

7x – 12y = -22 3x – 2y = 2-5x + 8y = 14 4x – 3y = 1

Solve the linear system using the linear combination method:

2x – y = 4 -4x + 8y = - 124x – 2y = 8 2x – 4y = 7

Solve the linear system using the linear combination method:

3x + 2y = -3 2x – 3y = 4-6x – 5y = 12 6x – 9y = -3

Homework:p. 142-143

8-24 even, 28, 30, 32