Solve the system by substitution.minus, 7, x, minus, 2, y, equals, minus, 38−7x−2y=−38minus, 3, y, equals, x−3y=x

Question

Solve the system by substitution.

Given the equations:

$-7x - 2y = -38$
$-3y = x$

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Solution

The system of equations is:

-7x - 2y = -38 -3y = x

Step 1: Solve the second equation for x:

x = -3y

Step 2: Substitute x = -3y into the first equation:

-7(-3y) - 2y = -38 21y - 2y = -38 19y = -38

Step 3: Solve for y:

y = -38 / 19 y = -2

Step 4: Substitute y = -2 into the second equation to solve for x:

x = -3(-2) x = 6

So, the solution to the system of equations is x = 6, y = -2.

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