Solve using substitution:

Find y in terms of x using the second equation:

5x-y=1

5x-1=y

Then plug this y into the first equation

2x^{2}+3x-2y=6

2x^{2}+3x-2(5x-1)=6

2x^{2}+3x-10x+2=6

2x^{2}-7x-4=0

(2x+1)(x-4)=0

2x+1=0 or x-4=0

2x=-1

x=-1/2 or x=4

Back substitute x=-1/2 back into either of the original equations to find the corresponding y-value

5x-y=1 , y=5x-1=5(-1/2)-1=-7/2

Back substitute x=4 back into either of the original equations to find the corresponding y-value

y=5x-1=5(4)-1=19

The two solutions are therefore (-1/2, -7/2) and (4, 19)