Intermediate Algebra (11th edition)

Solving a System by Elimination

Solve the system.

(1)

(2)

Step 1 Both equations are in standard form.

Step 2 Suppose that you wish to eliminate the variable x. One way to do this is to

multiply equation (1) by 2 and equation (2) by

2 times each side of equation (1)

- 10 x- 15 y=- 65 - 5 times each side of equation (2)

10 x- 4 y= 8

- 5.

2 x+ 3 y= 13

5 x- 2 y= 4

EXAMPLE 7

216 CHAPTER 4 Systems of Linear Equations

Solving a Linear System by Elimination

Step 1 Write both equations in standard form

Step 2 Make the coefficients of one pair of variable terms opposites.

Multiply one or both equations by appropriate numbers so that the

sum of the coefficients of either the x- or y-terms is 0.

Step 3 Addthe new equations to eliminate a variable. The sum should be

an equation with just one variable.

Step 4 Solvethe equation from Step 3 for the remaining variable.

Step 5 Find the other value.Substitute the result of Step 4 into either of

the original equations and solve for the other variable.

Step 6 Checkthe ordered-pair solution in bothof the originalequations.

Then write the solution set.

AxByC.

Step 3 Now add.

Add.

Step 4 Solve for y. Divide by.

Step 5 To find x, substitute 3 for yin either equation (1) or equation (2).

(2)

Let

Multiply.

Subtract 9.

Divide by 2.

Step 6 To check, substitute 2 for xand 3 for yin both equations (1) and (2).

CHECK (1) (2)

✓ True ✓ True

The solution set is 51 2, 3 26. NOW TRY

4 = 4 13 = 13

10 - 6  4 4 + 9  13

5122 - 2132  4 2122 + 3132  13

5 x- 2 y= 4 2 x+ 3 y= 13

x= 2

2 x= 4

2 x+ 9 = 13

2 x+ 3132 = 13 y=3.

2 x+ 3 y= 13

y= 3 - 19

- 19 y=- 57

-^10 x-^15 y=-^65

10 x- 4 y= 8

The goal is to

have opposite

coefficients.

NOW TRY
EXERCISE 7
Solve the system.

5 x+ 2 y= 10

2 x- 5 y= 4

NOW TRY ANSWER

7. 51 2, 0 26