Let's solve the system of linear equations given by:
[tex]\[
\begin{cases}
9x - 10y = -9 \\
5x + 10y = -5
\end{cases}
\][/tex]
To find the solution, follow these steps:
1. Label the equations:
[tex]\[
\begin{cases}
9x - 10y = -9 & \quad \text{(Equation 1)} \\
5x + 10y = -5 & \quad \text{(Equation 2)}
\end{cases}
\][/tex]
2. Add Equation 1 and Equation 2:
[tex]\[
(9x - 10y) + (5x + 10y) = -9 + (-5)
\][/tex]
Simplify the left-hand side:
[tex]\[
9x + 5x - 10y + 10y = -14
\][/tex]
Which reduces to:
[tex]\[
14x = -14
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-14}{14} = -1
\][/tex]
4. Substitute [tex]\(x = -1\)[/tex] back into one of the original equations to solve for [tex]\(y\)[/tex]. We will use Equation 2:
[tex]\[
5(-1) + 10y = -5
\][/tex]
Simplify:
[tex]\[
-5 + 10y = -5
\][/tex]
Add 5 to both sides:
[tex]\[
10y = 0
\][/tex]
Divide by 10:
[tex]\[
y = 0
\][/tex]
Hence, the solution to the system of equations is:
[tex]\[
(x, y) = (-1, 0)
\][/tex]
