Question

Solve using substitution.
-x - 2y = 8
-8x - 6y = 4
(_,_)

Answer 1

To solve the system of equations using substitution, we first rewrite one of the equations to express one variable in terms of the other. Let's start with the first equation:

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

We can solve for \(x\):

\[
-x = 8 + 2y
\]
\[
x = -8 - 2y
\]

Now we substitute \(x = -8 - 2y\) into the second equation:

2) \(-8x - 6y = 4\)

Substituting for \(x\):

\[
-8(-8 - 2y) - 6y = 4
\]

Now we simplify:

\[
64 + 16y - 6y = 4
\]
\[
64 + 10y = 4
\]

Next, we isolate \(y\):

\[
10y = 4 - 64
\]
\[
10y = -60
\]
\[
y = -6
\]

Now that we have \(y\), we substitute it back into the equation for \(x\):

\[
x = -8 - 2(-6)
\]
\[
x = -8 + 12
\]
\[
x = 4
\]

Thus, the solution to the system of equations is \((x, y) = (4, -6)\).

Final answer:
\[
(4, -6)
\]