The following system of equations is graphed below. y=(1)/(2)x+(5)/(2) y=-(2)/(3)x-1 Find the solution to the system. A. x=3,y=-3 B. x=3,y=4 C. x=-3,y=1 D. x=0,y=-1

The description of the graph provided does not match the system of equations given. However, to solve the system of equations, we do not need the graph. We can solve the system algebraically.The system of equations is:\[y = \frac{1}{2}x + \frac{5}{2}\]\[y = -\frac{2}{3}x - 1\]To find the solution, we can set the two equations equal to each other since they both equal y.Step 1: Set the equations equal to each other.\[\frac{1}{2}x + \frac{5}{2} = -\frac{2}{3}x - 1\]Step 2: Clear the fractions by finding a common denominator, which is 6 in this case, and multiply through by it.\[6 \cdot \left(\frac{1}{2}x + \frac{5}{2}\right) = 6 \cdot \left(-\frac{2}{3}x - 1\right)\]\[3x + 15 = -4x - 6\]Step 3: Add 4x to both sides to get all x terms on one side.\[3x + 4x + 15 = -4x + 4x - 6\]\[7x + 15 = -6\]Step 4: Subtract 15 from both sides to isolate the x term.\[7x + 15 - 15 = -6 - 15\]\[7x = -21\]Step 5: Divide by 7 to solve for x.\[x = \frac{-21}{7}\]\[x = -3\]Step 6: Substitute x = -3 into one of the original equations to solve for y. We can use the first equation.\[y = \frac{1}{2}(-3) + \frac{5}{2}\]\[y = -\frac{3}{2} + \frac{5}{2}\]\[y = \frac{5}{2} - \frac{3}{2}\]\[y = \frac{2}{2}\]\[y = 1\]The solution to the system is \(x = -3\) and \(y = 1\), which corresponds to option C.Final Answer: C. \(x = -3, y = 1\)