The correct system of equations for this is:
x - y = 6
3x + 4y = 4
The easiest way to find answer in a multiple choice problem like this is by looking at the answer to the system of equations. The solution set to a system is always where the two lines cross. Here, we see that cross at the point (4, -2). This means that if we put 4 in for x and - 2 in for y, it will make both equations true. The only example of both being true is the set of equations listed above. Below is the work for what happens when we put those values in.
First Equation
x - y = 6
(4) - (-2) = 6
4 + 2 = 6
6 = 6 (TRUE)
Second Equation
3x + 4y = 4
3(4) + 4(-2) = 4
12 - 8 = 4
4 = 4 (TRUE)
Since both are true in this version and none of the other systems, this must be the system graphed above.
