# How do you solve x-3y=4 and -3x+5y=-14 using substitution?

Mar 20, 2016

$y = 0.5$
$x = 5.5$

#### Explanation:

First, we rearrange one of the formulae to give us $x$ in terms of $y$ (or vice versa)
$x - 3 y = 4 \text{ }$ (Add $3 y$ to both sides)
$x = 4 + 3 y$

Now we can substitute in our value for $x$ into the other equation so that we only have one unknown, $y$.

Then you expand the bracket and simplify it to find $y$.

$- 3 x + 5 y = - 14$
$- 3 \left(4 + 3 y\right) + 5 y = - 14$

(expand the brackets)

$- 12 - 9 y + 5 y = - 14$

(simplify the $y$ terms)

$- 12 - 4 y = - 14$

(add $12$ to both sides)

$- 4 y = - 2$

(divide both sides by $- 4$ to isolate the $y$ term)

$y = - \frac{2}{-} 4$
$y = 0.5$

We then substitute the $y$ value into the original equation to find $x$ (you can use either of the equations for this)

$x = 4 + 3 y$
$x = 4 + \left(3 \times 0.5\right)$
$x = 4 + 1.5$
$x = 5.5$

Then we can use the other equation to check our answer.

$- 3 x + 5 y = - 14$
$- \left(3 \times 5.5\right) + \left(5 \times 0.5\right) = - 14$
$- 16.5 + 2.5 = - 14$
$- 14 = - 14$
So we know our answer is right!