We have the system of equations:
- \(-5x + 4y = 48\) (Equation 1)
- \(-5x - 8y = 24\) (Equation 2)
To solve this system, we can first isolate one of the variables using either of the equations. Let's start with Equation 1 and solve for \(y\):
From Equation 1: \[ -5x + 4y = 48 \] Adding \(5x\) to both sides gives: \[ 4y = 5x + 48 \] Now, divide by 4: \[ y = \frac{5x + 48}{4} \]
Next, we can substitute this expression for \(y\) into Equation 2:
Substituting \(y\) into Equation 2: \[ -5x - 8\left(\frac{5x + 48}{4}\right) = 24 \] Now, multiply each term in the equation by 4 to eliminate the fraction: \[ -20x - 8(5x + 48) = 96 \] Distributing \(-8\): \[ -20x - 40x - 384 = 96 \] Combining like terms: \[ -60x - 384 = 96 \] Adding 384 to both sides gives: \[ -60x = 480 \] Now divide by \(-60\): \[ x = -8 \]
Now we can find \(y\) by substituting \(x = -8\) back into the expression for \(y\): \[ y = \frac{5(-8) + 48}{4} \] Calculating inside the parentheses: \[ y = \frac{-40 + 48}{4} = \frac{8}{4} = 2 \]
Thus, the solution to the system of equations is: \[ (x, y) = (-8, 2) \]
Hence, the answer is \((-8, 2)\).