Solve the system of equations: ) -4x+6y=-58 4x-3y=31

To solve the system of equations, we can use the method of elimination. <br /><br />First, let's multiply the first equation by 3 and the second equation by 6 to make the coefficients of y in both equations equal:<br /><br />$\begin{cases} -12x + 18y = -174\\ 24x - 18y186\end{cases}$<br /><br />Now, we can add the two equations together to eliminate y:<br /><br />$12x = 12$<br /><br />Dividing both sides by 12, we get:<br /><br />$x = 1$<br /><br />Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. Let's use the first equation:<br /><br />$-4(1) + 6y = -58$<br /><br />Simplifying, we get:<br /><br />$-4 + 6y = -58$<br /><br />Adding 4 to both sides, we get:<br /><br />$6y = -54$<br /><br />Dividing both sides by 6, we get:<br /><br />$y = -9$<br /><br />Therefore, the solution to the system of equationsx1$ and $y = -9$.