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EXAMPLE 3

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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EXAMPLE 3

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  1. 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.

  2. (–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.

  3. 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).

  4. 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.

  5. 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

  6. 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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