SOLUTION: Solve each of the following systems by substitution. 5x- 2y = -5 y-5x =3

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Question 75600: Solve each of the following systems by substitution.
5x- 2y = -5
y-5x =3

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the 2nd equation for y
y-5x+=3
y=3%2B5x
Plug this into the y of the first equation
5x-+2%2Ahighlight%28%283%2B5x%29%29+=+-5
5x-+6-10x+=+-5 Distribute the -2
-5x-6=-5 Combine like terms
-5x%2Bcross%28-6%2B6%29=-5%2B6 Add 6 to both sides
cross%28-5%2F-5%29x=1%2F-5 Divide both sides by -5
x=-%281%2F5%29
Now plug this in for x to solve for y in the 1st equation:
5%28-1%2F5%29-+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%28-1%2F5%29-+2%282%29+=+-5
2-5%28-1%2F5%29+=3
-1-4+=+-5
2%2B1+=3
-5+=+-5 works
3+=3 works