Question

–8x − 5y = 8
x + 3y = 18

Answer 1

To solve the system of equations:

1. \( -8x - 5y = 8 \)
2. \( x + 3y = 18 \)

we can use the substitution or elimination method. Here, I'll use the elimination method.

First, let's rearrange the second equation to express \(x\) in terms of \(y\):

From equation 2:
\[
x = 18 - 3y
\]

Now we will substitute \(x\) from this equation into the first equation:

Substituting into equation 1:
\[
-8(18 - 3y) - 5y = 8
\]

Now distribute \(-8\):
\[
-144 + 24y - 5y = 8
\]

Combine like terms:
\[
-144 + 19y = 8
\]

Add \(144\) to both sides:
\[
19y = 152
\]

Now, divide by \(19\):
\[
y = 8
\]

Now that we have \(y\), substitute it back into the equation \(x = 18 - 3y\) to find \(x\):
\[
x = 18 - 3(8) = 18 - 24 = -6
\]

Thus, the solution to the system of equations is:
\[
x = -6, \quad y = 8
\]

The solution can be written as the point \((-6, 8)\).