Question: Solve using any method: \[ -6x - 3y = -12 \] \[ -4x - 2y = -8 \]

Solve using any method:

\[ -6x - 3y = -12 \]

\[ -4x - 2y = -8 \]

Solution

To solve the given system of equations using any method, let’s use the elimination method: First, write down the system of equations: \[ \begin{cases} -6x - 3y = -12 & \\ -4x - 2y = -8 & \end{cases} \] To eliminate one of the variables, multiply the second equation by 1.5 to make the coefficients of \(x\) equal: \[ \begin{cases} -6x - 3y = -12 & \\ -6x - 3y = -12 & \end{cases} \] Now, subtract the second equation from the first equation: \[ (-6x - 3y) - (-6x - 3y) = (-12) - (-12) \] This simplifies to: \[ 0 = 0 \] This outcome indicates that the two equations are dependent, meaning they represent the same line. Therefore, there are infinitely many solutions, as every point on the line is a solution to the system.