we have
Y=2x-13 -----> equation A
5x+3y=16 ----> equation B
step 1
Multiply the equation A by 3 both sides
3*Y=3*(2x-13) -----> 3y=6x-39 ------> equation C
step 2
Subtract B from equation C
3y=6x-39
-[5x+3y=16]
------------------
-5x=6x-39-16
solve for x
6x+5x=39+16
11x=55
x=5
step 3
Find the value of y
substitute the value of x in equation A
y=2(5)-13 ------> y=-3
therefore
x=5 and y=-3