Question

solve the system by substitution.
-6x - 2y = 20
3y = x

Explanation:

Step1: Substitute \( x = 3y \) into the first equation

We know from the second equation \( 3y = x \), so substitute \( x \) in \( -6x - 2y = 20 \) with \( 3y \). This gives us \( -6(3y) - 2y = 20 \).

Step2: Simplify and solve for \( y \)

First, calculate \( -6(3y) = -18y \), so the equation becomes \( -18y - 2y = 20 \). Combine like terms: \( -20y = 20 \). Then divide both sides by \( -20 \): \( y = \frac{20}{-20} = -1 \).

Step3: Substitute \( y = -1 \) back to find \( x \)

Using the equation \( x = 3y \), substitute \( y = -1 \). So \( x = 3(-1) = -3 \).

Answer:

The solution to the system is \( x = -3 \), \( y = -1 \)