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]
[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]
