Question

10x + 9y = –15
–2x − 2y = 2

(, )

Answer 1

To solve the system of equations:

1. \(10x + 9y = -15\) (Equation 1)
2. \(-2x - 2y = 2\) (Equation 2)

Let's first simplify Equation 2. Dividing the entire equation by -2 gives us:

\[
x + y = -1 \quad (Equation 2')
\]

Now we can express \(y\) in terms of \(x\) from Equation 2':

\[
y = -1 - x
\]

Next, we substitute \(y\) in Equation 1 with \(-1 - x\):

\[
10x + 9(-1 - x) = -15
\]

Distributing the 9:

\[
10x - 9 - 9x = -15
\]

Combining like terms:

\[
x - 9 = -15
\]

Adding 9 to both sides gives us:

\[
x = -15 + 9 = -6
\]

Now that we have \(x\), we can find \(y\) using Equation 2':

\[
y = -1 - (-6) = -1 + 6 = 5
\]

So, the solution to the system of equations is:

\[
(x, y) = (-6, 5)
\]

The final answer is:

\[
\boxed{(-6, 5)}
\]