Question

–9x − y = 9
x + 2y = 16

(, )
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Answer 1

To solve the system of equations:

1. **Equation 1:** \(-9x - y = 9\)
2. **Equation 2:** \(x + 2y = 16\)

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

First, let's solve Equation 1 for \(y\):

\[
-y = 9 + 9x
\]
\[
y = -9x - 9
\]

Now, substitute this expression for \(y\) into Equation 2:

\[
x + 2(-9x - 9) = 16
\]
\[
x - 18x - 18 = 16
\]
\[
-17x - 18 = 16
\]
\[
-17x = 16 + 18
\]
\[
-17x = 34
\]
\[
x = -2
\]

Now that we have the value of \(x\), we can substitute it back into the expression we found for \(y\):

\[
y = -9(-2) - 9
\]
\[
y = 18 - 9
\]
\[
y = 9
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-2, 9)
\]

So the answer is \((-2, 9)\).