Questions: 2x + 5y = -22 4x - 3y = 8

Solution Steps

To solve the system of linear equations, we can use the method of substitution or elimination. Here, we'll use the elimination method to eliminate one of the variables by making the coefficients of either \(x\) or \(y\) equal in both equations. Then, we'll solve for the remaining variable and substitute back to find the other variable.

We are given the following system of linear equations: \[ \begin{align_} 2x + 5y &= -22 \\ 4x - 3y &= 8 \end{align_} \]

To eliminate one of the variables, we can multiply the first equation by 2 to make the coefficients of \(x\) in both equations equal: \[ \begin{align_} 4x + 10y &= -44 \\ 4x - 3y &= 8 \end{align_} \]

Subtract the second equation from the first to eliminate \(x\): \[ (4x + 10y) - (4x - 3y) = -44 - 8 \] \[ 13y = -52 \]

Divide both sides by 13 to solve for \(y\): \[ y = \frac{-52}{13} = -4 \]

Substitute \(y = -4\) back into the first equation to solve for \(x\): \[ 2x + 5(-4) = -22 \] \[ 2x - 20 = -22 \] \[ 2x = -2 \] \[ x = \frac{-2}{2} = -1 \]

Final Answer