Question

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

Explanation:

Step1: Express x from the second equation

From \(-3y = x\), we have \(x=-3y\).

Step2: Substitute x into the first equation

Substitute \(x = - 3y\) into \(-7x-2y=-38\), we get \(-7(-3y)-2y=-38\).
Simplify the left - hand side: \(21y - 2y=-38\), which is \(19y=-38\).

Step3: Solve for y

Divide both sides of \(19y = - 38\) by 19: \(y=\frac{-38}{19}=-2\).

Step4: Solve for x

Substitute \(y = - 2\) into \(x=-3y\), then \(x=-3\times(-2) = 6\).

Answer:

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