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Solve the equation for y. STEP 1. x. y =. +. –. 9. 7. 4. 4. EXAMPLE 3. Rewrite a linear equation. Solve 9 x – 4 y = 7 for y . Then find the value of y when x = –5. SOLUTION. 9 x – 4 y = 7. Write original equation. –4 y = 7 – 9 x. Subtract 9 x from each side.

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Solve the equation for y.

STEP 1

x

y =

+

9

7

4

4

EXAMPLE 3

Rewrite a linear equation

Solve 9x – 4y = 7 for y. Then find the value ofywhen x= –5.

SOLUTION

9x – 4y = 7

Write original equation.

–4y = 7 – 9x

Subtract 9xfrom each side.

Divide each side by–4.


(–5)

9(–5) – 4(–13) 7

45

y =

4

y =

+

7

7

9

4

4

4

?

=

EXAMPLE 3

Rewrite a linear equation

Substitute the given value into the rewritten equation.

STEP 2

Substitute–5 forx.

Multiply.

y = –13

Simplify.

CHECK

9x– 4y= 7

Write original equation.

Substitute–5 for xand–13 for y.

7 = 7

Solution checks.


Solve the equation for y.

STEP 1

6

y =

2 + x

EXAMPLE 4

Rewrite a nonlinear equation

Solve 2y + xy = 6 for y. Then find the value of ywhen x= –3.

SOLUTION

2y + x y = 6

Write original equation.

(2+ x) y = 6

Distributive property

Divide each side by (2 + x).


Substitute the given value into the rewritten equation.

STEP 2

6

y =

2 + (–3)

EXAMPLE 4

Rewrite a nonlinear equation

Substitute –3 for x.

y = –6

Simplify.


ANSWER

ANSWER

ANSWER

y = 7 + 6x

+ 6

y = 19

y = 5

y = 3

3x

+

y =

2

y = –

x

13

5

5

for Examples 3 and 4

GUIDED PRACTICE

Solve the equation for y. Then find the value of ywhen x = 2.

8. y – 6x = 7

9. 5y – x = 13

10. 3x + 2y = 12


1

4

ANSWER

ANSWER

ANSWER

y =

y =

y =

2x

28

3 +x

5

2x

4 – x

y = –1

1

y =

y = 14

–1

5

for Examples 3 and 4

GUIDED PRACTICE

Solve the equation for y. Then find the value of ywhen x = 2.

12. 3 = 2xy – x

11. 2x + 5y = –1

13. 4y – xy = 28


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