Please print your full name in capital letters. 48 Name: Lydea Loevirer 1. (40 points) Use either method to find the solution to the following system, \[ \left\{\begin{array}{l}3 x-7 y=13 \\ 6 x+5 y=7 .\end{array}\right. \] Graph the two equations and mark the solution on the graph. If no solution, state so.

First, let's go through solving the system of equations step by step. 1. Start with the equations: \[ \left\{\begin{array}{l} 3x - 7y = 13 \\ 6x + 5y = 7 \end{array}\right. \] 2. We can use the substitution or elimination method. Here, we'll use the elimination method. 3. Multiply the first equation by 2 to align the coefficients of \(x\): \[ 6x - 14y = 26 \] 4. Now, rewrite the system: \[ \left\{\begin{array}{l} 6x - 14y = 26 \\ 6x + 5y = 7 \end{array}\right. \] 5. Subtract the second equation from the first: \[ (6x - 14y) - (6x + 5y) = 26 - 7 \] This simplifies to: \[ -19y = 19 \] Thus, \(y = -1\). 6. Substitute \(y = -1\) back into one of the original equations to find \(x\). Using the first equation: \[ 3x - 7(-1) = 13 \] Simplifies to: \[ 3x + 7 = 13 \implies 3x = 6 \implies x = 2 \] 7. The solution to the system is \((x, y) = (2, -1)\). To graph the equations, plot both lines on a graph. The intersection point, which is the solution \((2, -1)\), will be marked on the graph. If we were to analyze the graph of the two lines, they would intersect at this point, indicating that this system of equations has a unique solution: \((2, -1)\).