So we have 2x - y = 9 and 3y + x = 1. Take the first one, and solving for y gets us y = 2x - 9. Substitute this into the second equation, and you have 3(2x - 9) + x = 1. Simplifying the left hand side gets us 6x - 27 + x = 1. 7x = 28. x = 4. Put this into either one, (I'm going to use the first) and you get 2(4) - y = 9,
8 - y = 9, -y = 1, so y = -1 and you can check this by putting both values of x and y into either equation.
x = 4
y = -1
Hope this helps!