I would do subsitute
solve for x in first tequation
x+4y=3
minus 4y both sides
x=3-4y
sub 3-4y for x in other equation
2x-3y=17
2(3-4y)-3y=17
6-8y-3y=17
6-11y=17
minus 6 both sides
-11y=11
divide both sides by -11
y=-1
sub back
x=3-4y
x=3-4(-1)
x=3+4
x=7
x=7
y=-1
(x,y)
(7,-1)