Question

Solve the system by substitution.
minus, 8, x, minus, y, equals, 30
−8x−y=
30
minus, 2, y, equals, x
−2y=
x

Answer 1

To solve the system of equations by substitution, we first need to rewrite the equations in a clearer form:

1. \(-8x - y = 30\)
2. \(-2y = x\)

Let's express \(x\) in terms of \(y\) using the second equation:

\[
x = -2y
\]

Now that we have \(x\) in terms of \(y\), we can substitute this expression for \(x\) into the first equation. Substitute \(-2y\) for \(x\) in the first equation:

\[
-8(-2y) - y = 30
\]

This simplifies to:

\[
16y - y = 30
\]

Combining like terms:

\[
15y = 30
\]

Now, divide both sides by 15:

\[
y = 2
\]

Now that we have the value of \(y\), we can substitute it back into the equation \(x = -2y\) to find \(x\):

\[
x = -2(2) = -4
\]

So the solution to the system of equations is:

\[
x = -4, \quad y = 2
\]

In conclusion, the solution is:

\[
(x, y) = (-4, 2)
\]