Question: 16) $6x - 12y = 24$ $-x - 6y = 4$ $6x + 36y = 24$

Solution

To solve the system of equations: \[ \begin{cases} 6x - 12y = 24 & \\ -x - 6y = 4 & \end{cases} \] First, let’s solve the second equation for \(x\): \[ -x - 6y = 4 \] Add \(x\) to both sides: \[ -6y = x + 4 \] Subtract 4 from both sides: \[ x = -6y - 4 \] Now substitute \(x = -6y - 4\) into the first equation: \[ 6(-6y - 4) - 12y = 24 \] Expand the equation: \[ -36y - 24 - 12y = 24 \] Combine like terms: \[ -48y - 24 = 24 \] Add 24 to both sides: \[ -48y = 48 \] Divide by -48: \[ y = -1 \] Substitute \(y = -1\) back into \(x = -6y - 4\): \[ x = -6(-1) - 4 \] Simplify: \[ x = 6 - 4 \] \[ x = 2 \] The solution to the system is \(x = 2\) and \(y = -1\).