Question: 6) \( x + 8y = 18 \) \(-7x + 4y = -6\)

Solution

To solve the given system of equations: \[ \begin{cases} x + 8y = 18 & \\ -7x + 4y = -6 & \end{cases} \] First, solve the first equation for \(x\): \[ x = 18 - 8y \] Substitute this expression for \(x\) in the second equation: \[ -7(18 - 8y) + 4y = -6 \] Expand the equation: \[ -126 + 56y + 4y = -6 \] Combine like terms: \[ 60y - 126 = -6 \] Add 126 to both sides: \[ 60y = 120 \] Divide by 60: \[ y = 2 \] Substitute \(y = 2\) back into the expression for \(x\): \[ x = 18 - 8(2) \] Calculate: \[ x = 18 - 16 = 2 \] The solution is: \[ \begin{cases} x = 2 & \\ y = 2 & \end{cases} \]