How do you solve the following system using substitution?: 5x – 2y = -5, y – 5x = 3

1 Answer
May 28, 2018

x = (-1/5)
y = 2

Explanation:

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

Solving by Substitution

First, you want to find the equation for a variable that you can replace in the system. y - 5x = 3 is an equation that appears easy to re-arrange to get an equation for a variable, so we'll use it:

y - 5x = 3

Add 5x to both sides to cancel out -5x in order to get the equation for the value of y. You should now have:

y = 5x + 3

Now that you have an equation for a variable, substitute these terms (5x + 3) in the first equation of the system. So:

5x - 2y = -5 becomes
5x -2(5x + 3) = -5.

Distribute -2 to the terms inside the parentheses. You do this by multiplying -2 by each term, so:

-2 * 5x = -10x
-2 * 3 = -6

Re-write your equation to reflect new information:

5x -10x - 6 = -5

Combine like terms.

-5x - 6 = -5

Add 6 to both sides to cancel out -6. You should now have:

-5x = 1

Divide by -5 to isolate for x#. You should now have:

x = -1/5

Plug the value of x into the equation for the value of y:

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

Plug these values back in to confirm that they're right:
5x - 2y = -5
5(-1/5) - 2(2) = -5
-1 - 4 = -5
-5 = -5

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

These values are correct.