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–6 x – 9 y = –15. EXAMPLE 1. Multiply one equation , then add. Solve the linear system:. 6 x + 5 y = 19. Equation 1. 2 x + 3 y = 5. Equation 2. SOLUTION. STEP 1. Multiply Equation 2 by –3 so that the coefficients of x are opposites. 6 x + 5 y = 19. 6 x + 5 y = 19.

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SOLUTION

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Solution

–6x – 9y = –15

EXAMPLE 1

Multiply one equation, then add

Solve the linear system:

6x + 5y = 19

Equation 1

2x + 3y = 5

Equation 2

SOLUTION

STEP 1

Multiply Equation 2 by –3 so that the coefficients of x are opposites.

6x + 5y = 19

6x + 5y = 19

2x + 3y = 5

STEP 2

Add the equations.

–4y = 4


Solution

EXAMPLE 1

Multiply one equation, then add

STEP 3

Solve for y.

y = –1

STEP 4

Substitute –1 for yin either of the original equations and solve for x.

2x + 3y= 5

Write Equation 2.

2x + 3(–1) = 5

Substitute–1 for y.

2x + (–3) = 5

Multiply.

Subtract –3 from each side.

2x = 8

x = 4

Divide each side by 2.


Solution

?

2(4)+ 3(–1) = 5

?

6(4) +5(–1)= 19

19 = 19

5 = 5

EXAMPLE 1

Multiply one equation, then add

The solution is (4, –1).

ANSWER

CHECK

Substitute 4 for xand –1 for y in each of the original equations.

Equation 2

Equation 1

6x+ 5y= 19

2x+ 3y= 5


Solution

EXAMPLE 2

Multiply both equations, then subtract

Solve the linear system:

4x + 5y = 35

Equation 1

2y = 3x – 9

Equation 2

SOLUTION

STEP 1

Arrange the equations so that like terms are in columns.

4x + 5y = 35

Write Equation 1.

–3x + 2y = –9

Rewrite Equation 2.


Solution

8x + 10y = 70

–15x +10y = –45

x = 5

EXAMPLE 2

Multiply both equations, then subtract

STEP 2

Multiply Equation 1 by 2 and Equation 2 by 5 so that the coefficient of yin each equation is the least common multiple of 5 and 2, or 10.

4x + 5y = 35

–3x + 2y = –9

Subtract: the equations.

STEP 3

23x = 115

Solve: for x.

STEP 4


Solution

ANSWER

The solution is (5, 3).

EXAMPLE 2

Multiply both equations, then subtract

STEP 5

Substitute 5 for xin either of the original equations and solve for y.

4x+ 5y = 35

Write Equation 1.

4(5)+ 5y = 35

Substitute 5 forx.

y = 3

Solve for y.


Solution

?

2(3)= 3(5) – 9

?

4(5)+ 5(3)= 35

ANSWER

The solution is (5, 3).

35= 35

6= 6

EXAMPLE 2

Multiply both equations, then subtract

Substitute 5 for xand 3 for yin each of the original equations.

CHECK

Equation 2

Equation 1

2y= 3x– 9

4x+ 5y= 35


Solution

1.

6x – 2y = 1

ANSWER

The solution is (–0.5, –2).

for Examples 1 and 2

GUIDED PRACTICE

Solve the linear system using elimination.

–2x + 3y =–5


Solution

2.

2x + 5y = 3

ANSWER

The solution is (9, –3).

for Examples 1 and 2

GUIDED PRACTICE

Solve the linear system using elimination.

3x + 10y =–3


Solution

3x –7y = 5

3.

ANSWER

The solution is (–10, –5).

for Examples 1 and 2

GUIDED PRACTICE

Solve the linear system using elimination.

9y =5x + 5


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