Question

solve the system by substitution.

$-y = x$
$-7x - 5y = -20$

Explanation:

Step1: Substitute \( x = -y \) into the second equation

We have the second equation \( -7x - 5y = -20 \). Substituting \( x=-y \) into it, we get \( -7(-y) - 5y = -20 \).

Step2: Simplify the equation

Simplify \( -7(-y) - 5y = -20 \), which becomes \( 7y - 5y = -20 \), then \( 2y = -20 \).

Step3: Solve for \( y \)

Divide both sides of \( 2y = -20 \) by 2, we get \( y = -10 \).

Step4: Solve for \( x \)

Since \( x = -y \), substituting \( y = -10 \) into it, we get \( x = -(-10)=10 \).

Answer:

The solution to the system is \( x = 10 \), \( y = -10 \)