How do you solve this system of equations: #5x - 2y = 0 and - 4x + 3y = 7#?

1 Answer
Camilleon
May 22, 2018

x = 2
y = 5

Explanation:

#5x - 2y = 0#
#-4x + 3y = 7#

Substitution Method

First, we're going to take one of the two equations and get an equation for a variable. This'll be plugged into the second equation. Don't freak out, though. We'll do it step-by-step:

Let's find an equation for y.

#5x - 2y = 0#

First, let's subtract 5x from both sides to help us get to isolating for y.

#-2y = -5x#

Now, divide by -2 to isolate for y:

#y# = #-5/-2#x

Because two negatives create a positive:

#y# = #5/2##x#

Now, substitute this into the second equation where y is:

#-4x + 3y = 7#
#-4x + 3(5/2x) = 7#

Distribute.

#-4x + (15/2x) = 7#

Combine like terms. Converting 15/2 from fraction form to decimal form may help.

#-4x + 7.5x = 7# becomes #3.5x = 7#.

Divide by 3.5 to isolate for x.

#x = 2

Now, plug x back into your equation for y:

#y# = #5/2##(2)#

#y = 10/2, or 5#

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