Find the coordinates of the points of intersection of the graphs without building them: 5x–4y=16 and x–2y=6

we have that
equation 1
5x–4y=16
and
equation 2
x–2y=6

we know that

Part A) the x-intercept is when y=0
equation 1
5x–4y=16
for y=0
5x=16--------> x=16/5---> x=3.2
the point is (3.2,0)

equation 2
x–2y=6
for y=0
x=6
the point is (6,0)

Part B) the y-intercept is when x=0
equation 1
5x–4y=16
for x=0
-4y=16-------> y=-4
the point is (0,-4)

equation 2
x–2y=6
for x=0
-2y=6------> y=-3
the point is (0,-3)

the answer is
the coordinates of the points of intersection are
equation 1
5x–4y=16
(3.2,0)  and (0,-4)

equation 2
x–2y=6
(6,0) and (0,-3)