I don't know if you want to solve by elimination or substitution, so I will choose the easiest;) If you want the other repost and I will do it another way.
2x - y = 4
5x - y = 13
Looking at the equations, the easiest way to solve is by elimination because the y's line up already.
Since the signs on the y's are the same we will subtract the second line from the first line.
2x - y = 4
-(5x -y = 13)
-3x = 0 = -9 (2x -5x =-3x, -y--y=0, 4-13=-9)
To get x by itself, divide both sides by -3
-3x = -9
x = 3 (negative divided by negative is positive)
To calculate y, put x=3 into either equation. I will put it in the first one.
2 (3) - y = 4
6 - y = 4
y+ 6 - y = 4 + y (I want y positive, so I add y to both sides)
6 = 4 + y
-4 + 6 = 4 + y -4 (I want y by itself, so I subtract 4 from both sides)
2 = y
So my POI (point of intersection) is (3,2)
Normally, a lot of people end there, but I always like to check my answers to prove that I didn't make any silly mistakes.
To do this, I do a left side right side comparison using the equation that I didn't use to solve for the second variable.
Left Side Right Side
5x - y 13
5(3) - 2 13
15 - 2 13
13 = 13
I just proved that I did it all correctly. It the left side didn't equal the right side, I would go back and find my error and recheck it with my left side right side check.