Question: 5) $6x - 3y = 7$ $-2x + y = -8$

Solution

To solve the system of equations, let’s use the substitution or elimination method. Here, we’ll use the elimination method. First, let’s write down the system of equations: \[ \begin{cases} 6x - 3y = 7 & \\ -2x + y = -8 & \end{cases} \] We can eliminate \(y\) by making the coefficients of \(y\) in both equations opposites. We multiply the second equation by 3: \(-2x + y = -8\) becomes: \[ -6x + 3y = -24 \] Now, add this to the first equation: \[ \begin{align*} (6x - 3y) + (-6x + 3y) &= 7 + (-24) \\ 0 &= -17 \end{align*} \] This results in a contradiction, which means that the system of equations has no solution. The lines are parallel and do not intersect.