Question

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

Answer 1

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`