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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. Solve the equation for y. STEP 1 Substitute the given value into the rewritten equation. STEP 2 for Examples 3 and 4 GUIDED PRACTICE Solve the equation for y. Then find the value of ywhen x = 2. 8. y – 6x = 7 y – 6x = 7 y = 7 + 6x y = 7 + 6 (2) Substitute 2 forn. y = 7 + 12 Multiply. y = 19 Add.

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

  7. Solve the equation for y. STEP 1 + 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. 9. 5y – x = 13 5y – x = 13 Write original equation 5y = 13 + x Add xto each side Divide each side by 5

  8. 5(5) – 2 7 + y = 2 13 5 5 ? = for Examples 3 and 4 GUIDED PRACTICE Substitute the given value into the rewritten equation. STEP 2 Substitute 2 forn. y = 5 Simplify. CHECK 5y–x= 13 Write original equation. Substitute 2 for xand 19 for y. Solution checks. 3 = 3

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

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

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

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

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

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

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

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

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