Solve the following simultaneous equations: 3x + 5y = 19 and 8x - 2y = -18. If both equations represent lines in a coordinate system, at which point do they intersect?

I. 3x + 5y = 19 II. 8x - 2y = -18 . We see that we can simplify the second equation, and we do so: II. x - y = -9. Now, we check to see which variable is the easiest to solve for in the system of equations. In this case, I will choose y in the second, as that one is easy and produces a nicer value to work with than the others. We solve for y in the second equation: y = 9+4x. Substitute y value into the first equation: 3x + 5(9+4x) = 19, then 3x + 45 + 20x = 19, then 23x = -26 so x = -26/23. Now, we can substitute x into equation two and solve: 4(-26/23) - 2y = -9, then (-104/23) - 2y = -9, so y = 103/23. Therefore, x = -26/23, and y = 103/23. (x,y) is the point where the two lines that the equations represent will cross. So the two lines intersect at point (-26/23,103/23).