Question

Solve.

–8x + 7y = 18
3x − y = –10

Answer 1

To solve the system of equations:

1. \(-8x + 7y = 18\) (Equation 1)
2. \(3x - y = -10\) (Equation 2)

We can use the substitution or elimination method. Here, I'll use substitution. First, we solve Equation 2 for \(y\):

\[
y = 3x + 10
\]

Now, substitute \(y\) in Equation 1:

\[
-8x + 7(3x + 10) = 18
\]

Distributing \(7\):

\[
-8x + 21x + 70 = 18
\]

Combine like terms:

\[
13x + 70 = 18
\]

Now, isolate \(x\) by subtracting \(70\) from both sides:

\[
13x = 18 - 70
\]
\[
13x = -52
\]

Now, divide by \(13\):

\[
x = -4
\]

Next, substitute \(x = -4\) back into the expression for \(y\):

\[
y = 3(-4) + 10
\]
\[
y = -12 + 10
\]
\[
y = -2
\]

Thus, the solution to the system of equations is:

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

We can write the solution as \((-4, -2)\).