Question

what value of y is a solution to this equation?
5y + 7y - 20 = 64
y = -9
y = 7
submit

Explanation:

Step1: Combine like terms

Combine the \( y \)-terms: \( 5y + 7y = 12y \), so the equation becomes \( 12y - 20 = 64 \).

Step2: Add 20 to both sides

Add 20 to each side: \( 12y - 20 + 20 = 64 + 20 \), which simplifies to \( 12y = 84 \).

Step3: Divide by 12

Divide both sides by 12: \( \frac{12y}{12} = \frac{84}{12} \), so \( y = 7 \).

We can also check by substituting \( y = -9 \) into the original equation: \( 5(-9) + 7(-9) - 20 = -45 - 63 - 20 = -128
eq 64 \), so \( y = -9 \) is not a solution. Substituting \( y = 7 \): \( 5(7) + 7(7) - 20 = 35 + 49 - 20 = 64 \), which matches the right side.

Answer:

\( y = 7 \)