Solve each of the following systems by substitution.?

Question

5x - 2y= -5
y - 5x = 3

Answer 1

5x - 2y = -5
y - 5x = 3

First, put them both in the form ax + by = c

5x - 2y = -5
-5x + y = 3

To solve by substitution, choose any of the two equations and solve for one variable in terms of the other. Since there is less operations involved, I'm going to choose the second equation.

-5x + y = 3
y = 3 + 5x

Now, I'm going to plug y = 3 + 5x into the first equation,
5x - 2y = -5.

5x - 2(3 + 5x) = -5

Now, solve for x.

5x - 6 - 10x = -5
-5x - 6 = -5
-5x = -5 + 6
-5x = 1
x = (-1/5)

Now that we have one variable, we can solve for the other easily. Recall that we calculated y = 3 + 5x. Plug in x = (-1/5), and we get
y = 3 + 5(-1/5)
y = 3 + (-5/5)
y = 3 - 1
y = 2

That means our solution is x = -1/5, y = 2

Answer 2

5x-2y=-5
y-5x=3 >> y=3+5x

5x-2(3+5x)=-5
5x-10x-6=-5
-5x=1
x=-1/5

y=3+5(-1/5)
y=3+-1
y=2

x=-1/5 and y=2