Question

solve the system by substitution.

$-10x + 2y = -32$
$9x = y$

Explanation:

Step1: Substitute \( y = 9x \) into the first equation

We know from the second equation that \( y = 9x \). Substitute this into \( -10x + 2y = -32 \), so we get \( -10x + 2(9x) = -32 \).

Step2: Simplify and solve for \( x \)

Simplify the left - hand side of the equation: \( -10x+18x=-32 \), which combines to \( 8x=-32 \). Then divide both sides by 8: \( x=\frac{-32}{8}=-4 \).

Step3: Find the value of \( y \)

Substitute \( x = - 4 \) into \( y = 9x \), so \( y=9\times(-4)=-36 \).

Answer:

The solution to the system is \( x=-4 \), \( y = - 36 \) (or the ordered pair \((-4,-36)\))