Rewrite a linear equation

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Presentation transcript:

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.

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.

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).

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.

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 = 7 + 6x Substitute the given value into the rewritten equation. STEP 2 y = 7 + 6 (2) Substitute 2 for n. y = 7 + 12 Multiply. y = 19 Add.

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.

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

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) – 2 7 = ? Substitute 2 for x and 19 for y. 3 = 3 Solution checks.

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

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.

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 –

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.

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

( ) 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 1 for y. 5 4 3 = 3 Solution checks.

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)

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.