Question

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solve the system by substitution.
$-7x - 2y = -38$
$-3y = x$

Explanation:

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

We have the first equation \(-7x - 2y = -38\) and the second equation gives \( x=-3y \). Substitute \( x \) in the first equation:
\(-7(-3y)-2y=-38\)

Step2: Simplify and solve for \( y \)

Simplify the left - hand side: \( 21y-2y=-38 \), which is \( 19y=-38 \).
Divide both sides by 19: \( y=\frac{-38}{19}=-2 \)

Step3: Solve for \( x \) using \( x = - 3y \)

Substitute \( y = - 2 \) into \( x=-3y \): \( x=-3\times(-2)=6 \)

Answer:

The solution of the system is \( x = 6 \), \( y=-2 \)