What is the solution to the system of equations? ) -2x+3y=13 3x+4y=6 (-2,3) C (-(7)/(2),2) (3,-2) (-11,3)

To solve the system of equations, we can use the method of substitution or elimination. Let's use the elimination method.

First, we can multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations equal:

$$\begin{cases} -6x + 9y = 39\\ 6x + 8y = 12\end{cases}$$

Next, we can add the two equations together to eliminate x:

$$-6x + 9y + 6x + 8y = 39 + 12$$

$$17y = 51$$

Dividing both sides by 17, we get:

$$y = 3$$

Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

$$-2x + 3(3) = 13$$

$$-2x + 9 = 13$$

Subtracting 9 from both sides, we get:

$$-2x = 4$$

Dividing both sides by -2, we get:

$$x = -2$$

Therefore, the solution to the system of equations is $$(-2, 3)$$ .