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

2. Rewrite a linear equation
EXAMPLE 3
Rewrite a linear equation
STEP 2
Substitute the given value into the rewritten equation.
y = 9 4 7 – +
(–5)
Substitute –5 for x.
y = 45 4 7 –
Multiply.
y = – 13
Simplify.
CHECK
9x – 4y = 7
Write original equation.
9(– 5) – 4(– 13) 7 = ?
Substitute –5 for x and –13 for y.
7 = 7
Solution checks.

3. Rewrite a nonlinear equation
EXAMPLE 4
Rewrite a nonlinear equation
Solve 2y + xy = 6 for y. Then find the value of y when x = –3.
SOLUTION
Solve the equation for y.
STEP 1
2y + x y = 6
Write original equation.
(2+ x) y = 6
Distributive property
y = 6
2 + x
Divide each side by ( 2 + x).

4. Rewrite a nonlinear equation
EXAMPLE 4
Rewrite a nonlinear equation
Substitute the given value into the rewritten equation.
STEP 2
y = 6
2 + (– 3)
Substitute – 3 for x.
y = – 6
Simplify.

5. Solve the equation for y. Then find the value of y when x = 2.
GUIDED PRACTICE
for Examples 3 and 4
Solve the equation for y. Then find the value of y when x = 2.
8. y – 6x = 7
Solve the equation for y.
STEP 1
y – 6x = 7
y = x
Substitute the given value into the rewritten equation.
STEP 2
y = (2)
Substitute 2 for n.
y =
Multiply.
y = 19
Add.

6. GUIDED PRACTICE for Examples 3 and 4 CHECK y – 6x = 7 19 – 6 (2) 7 =
Write original equation.
19 – 6 (2) 7 = ?
Substitute 2 for x and 19 for y.
7 = 7
Solution checks.

7. Solve the equation for y. Then find the value of y when x = 2.
GUIDED PRACTICE
for Examples 3 and 4
Solve the equation for y. Then find the value of y when x = 2.
9. 5y – x = 13
Solve the equation for y.
STEP 1
5y – x = 13
Write original equation
5y = 13 + x
Add x to each side
y = x 5 13 +
Divide each side by 5

8. Substitute the given value into the rewritten equation.
GUIDED PRACTICE
for Examples 3 and 4
STEP 2
Substitute the given value into the rewritten equation.
y = 2 5 13 +
Substitute 2 for n.
y = 5
Simplify.
CHECK
5y – x = 13
Write original equation.
5(5) – = ?
Substitute 2 for x and 19 for y.
3 = 3
Solution checks.

9. Solve the equation for y. Then find the value of y when x = 2.
GUIDED PRACTICE
for Examples 3 and 4
Solve the equation for y. Then find the value of y when x = 2.
10. 3x + 2y = 12
Solve the equation for y.
STEP 1
3x + 2y = 12
Write original equation
5y = 12 – 3x
Subtract 3x from each side
y = 3x 2 12 +
Divide each side by 2
= – 3x 2
+ 6

10. Substitute the given value into the rewritten equation.
GUIDED PRACTICE
for Examples 3 and 4
STEP 2
Substitute the given value into the rewritten equation.
y =
(2) 2 + 6
– 3
Substitute 2 for n.
y =
– 2 2 + 6
Multiply
y = 3
Simplify
CHECK
3x – yx = 12
Write original equation.
3(2) + 2(3) 12 = ?
Substitute 3 for y and 2 for x.
12 = 12
Solution checks.

11. Solve the equation for y. Then find the value of y when x = 2.
GUIDED PRACTICE
for Examples 3 and 4
Solve the equation for y. Then find the value of y when x = 2.
11. 2x + 5y = –1
Solve the equation for y.
STEP 1
2x + 5y = –1
Write original equation
5y = –1 – 2x
Subtract 2x from each side
y = 2x 5 –1 –
Divide each side by 5 = 2x 5 –1 –

12. Substitute the given value into the rewritten equation.
GUIDED PRACTICE
for Examples 3 and 4
STEP 2
Substitute the given value into the rewritten equation.
y =
– 1 2 –
2(2) 5
Substitute 2 for n.
y =
– 1 5 – 4
Multiply
y = – 1
Simplify
CHECK
2x + 5y = –1
Write original equation.
2(2) + 5(–1) –1 = ?
Substitute 2 for x and –1 for y.
–1 = –1
Solution checks.

13. Solve the equation for y. Then find the value of y when x = 2.
GUIDED PRACTICE
for Examples 3 and 4
Solve the equation for y. Then find the value of y when x = 2.
12. 3 = 2xy – x
Solve the equation for y.
STEP 1
3 = 2xy – x
Write original equation
3 + x = 2xy
Add x to each side
= y
3 +x 2x
Divide 2x to each side

14. ( ) GUIDED PRACTICE for Examples 3 and 4 STEP 2
Substitute the given value into the rewritten equation.
= y
3 + 2
2 (2)
Substitute 2 for n.
y = 5 4 = 1
Simplify
CHECK
3= 2xy –x
Write original equation.
3 2(2) – (2) = ?
( ) 5 4
Substitute 2 for x and for y. 5 4
3 = 3
Solution checks.

15. Solve the equation for y. Then find the value of y when x = 2.
GUIDED PRACTICE
for Examples 3 and 4
Solve the equation for y. Then find the value of y when x = 2.
13. 4y – xy = 28
Solve the equation for y.
STEP 1
4y – xy = 28
Write original equation
(4 – x)y = 28
Distributive property 28
4 – x
= y
Divide each side by (4 – x)

16. Substitute the given value into the rewritten equation.
GUIDED PRACTICE
for Examples 3 and 4
STEP 2
Substitute the given value into the rewritten equation. 28
4 – 2
y =
Substitute 2 for x.
y = 14
Simplify
CHECK
4y –xy = 28
Write original equation.
4(14) – (2) (14) 28 = ?
Substitute 14 for y and 2 for y.
28 = 28
Solution checks.