# How do you solve 0.07 x - 0.01 y = 1.6  and 0.26x + 0.18 y = 16.8 using substitution?

Apr 9, 2017

$x = 30$ and $y = 50$

#### Explanation:

First, we must rewrite the two equations and make sure they have an identical term. I will rewrite them as follows:

$0.07 x - 0.01 y = 1.6$ will become $- 1.26 x + 0.18 y = - 28.8$

$0.26 x + 0.18 y = 16.8$ will stay the same.

Now as you can see, both equations now have $0.18 y$ in common. We will use this to substitute.

We will rewrite one equation, let's use the first one, to isolate $0.18 y$.

$- 1.26 x + 0.18 y = - 28.8$ will become $0.18 y = - 28.8 + 1.26 x$

Now we can substitute this into the second equation to find the first variable.

$0.26 x + 0.18 y = 16.8$
$0.26 x + \left(- 28.8 + 1.26 x\right) = 16.8$
$0.26 x - 28.8 + 1.26 x = 16.8$
$1.52 x - 28.8 = 16.8$
$1.52 x = 45.6$
$x = 30$

Now that we have found the value of $x$, we can move on to substitute this value to find $y$.

Take an original question, we'll use the first one, and substitute our $x$ value.

$0.07 x - 0.01 y = 1.6$
$0.07 \left(30\right) - 0.01 y = 1.6$
$2.1 - 0.01 y = 1.6$
$- 0.01 y = - 0.5$
$y = 50$

So now we have solved the two equations to get $x = 30$ and $y = 50$.