Question

–x + 8y = 10
7x + 9y = –5

Answer 1

To solve the system of equations:

1. \(-x + 8y = 10\) (Equation 1)
2. \(7x + 9y = -5\) (Equation 2)

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

First, let's multiply Equation 1 by 7 to help eliminate \(x\):

\[
7(-x + 8y) = 7(10)
\]
\[
-7x + 56y = 70 \quad \text{(Equation 3)}
\]

Now, we'll leave Equation 2 as it is and have:

3. \(-7x + 56y = 70\)
4. \(7x + 9y = -5\)

Now we can add Equation 3 and Equation 4:

\[
(-7x + 56y) + (7x + 9y) = 70 + (-5)
\]
\[
0x + 65y = 65
\]

Now we can simplify:
\[
65y = 65
\]
\[
y = 1
\]

Now that we have \(y\), we can substitute it back into Equation 1 to find \(x\):

\[
-x + 8(1) = 10
\]
\[
-x + 8 = 10
\]
\[
-x = 10 - 8
\]
\[
-x = 2
\]
\[
x = -2
\]

Thus, the solution to the system of equations is:
\[
x = -2, \quad y = 1
\]

The solution can be written as the ordered pair \((-2, 1)\).