Question 75600
Solve the 2nd equation for y
{{{y-5x =3}}}
{{{y=3+5x}}}
Plug this into the y of the first equation
{{{5x- 2*highlight((3+5x)) = -5}}}
{{{5x- 6-10x = -5}}} Distribute the -2
{{{-5x-6=-5}}} Combine like terms
{{{-5x+cross(-6+6)=-5+6}}} Add 6 to both sides
{{{cross(-5/-5)x=1/-5}}} Divide both sides by -5
{{{x=-(1/5)}}}
Now plug this in for x to solve for y in the 1st equation:

{{{5(-1/5)- 2y = -5}}} Plug in x=-1/5
{{{-1-2y=-5}}} 
{{{-2y=-4}}} Add 1 to both sides
{{{y=2}}} Divide both sides by -2

So the solution is (-1/5,2)

Check:
{{{5x- 2y = -5}}}
{{{y-5x =3}}}
Plug in (-1/5,2)
{{{5(-1/5)- 2(2) = -5}}}
{{{2-5(-1/5) =3}}}

{{{-1-4 = -5}}}
{{{2+1 =3}}}

{{{-5 = -5}}} works
{{{3 =3}}} works