Answer :

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]