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Solving Linear and Nonlinear Equations for y: Step-by-Step Guide

This guide provides clear steps to solve both linear and nonlinear equations for y. It includes detailed examples such as rewriting the equations, substituting values, and checking the solutions. Users can learn how to deal with expressions like 9x - 4y = 7 and 2y + xy = 6, transforming them into forms easy to manipulate. Additional practice problems are provided at the end for further mastery of the concept, making it ideal for students looking to enhance their algebra skills.

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Solving Linear and Nonlinear Equations for y: Step-by-Step Guide

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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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