So to solve for x and y you need to add the two equations together, and to do this when you add them either the x or the y need to cross out.
For this equation we’re going to multiply the bottom equation by 2 so that the y’s will cancel out when we ad the equations together so that we can solve for x
5x-4y=19
2(x+2y=8)
Distribute the 2
5x-4y=19
2x+4y=16
Next add the two equations together
7x=35
As you can see the y was cancelled out. Now divide each side by 7 to solve for x
x=5
Now take this answer and plug it back into either equation to solve for y. I am going to plug it into the second equation, but you can choose either
x+2y=8
Replace x with its value, 5
5+2y=8
Subtract 5 from each side
2y=3
Divide each side by 2
y=3/2 (or 1.5)
ANSWER:
x = 5
y = 3/2 (or 1.5)