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

May 22, 2018

x = 2
y = 5

#### Explanation:

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

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.

$5 x - 2 y = 0$

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

$- 2 y = - 5 x$

Now, divide by -2 to isolate for y:

$y$ = $- \frac{5}{-} 2$x

Because two negatives create a positive:

$y$ = $\frac{5}{2}$$x$

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

$- 4 x + 3 y = 7$
$- 4 x + 3 \left(\frac{5}{2} x\right) = 7$

Distribute.

$- 4 x + \left(\frac{15}{2} x\right) = 7$

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

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

Divide by 3.5 to isolate for x.

#x = 2

Now, plug x back into your equation for y:

$y$ = $\frac{5}{2}$$\left(2\right)$

$y = \frac{10}{2} , \mathmr{and} 5$