# How do you solve the system x= 175+15y, .196x= 10.4y, z=10*y?

Oct 18, 2016

$x = 53.05$
$y = - 8.13$
$z = - 81.3$

#### Explanation:

To begin, plug in a equation for a variable that is already isolated. There are two variables that are already isolated, and those are $x \mathmr{and} z$. You could choose either to work with, doesn't matter, but I'm going to use $x$

So, plug the equation for $x$ into another equation that has that same variable in it. Which would be:

$.196 x = 10.4 y$

To begin, plug $x$ equation into $.196 x = 10.4 y$

$.196 \left(175 + 15 y\right) = 10.4 y$

Distribute $.196$ throughout the set of parenthesis

$34.3 + 2.94 y = 10.4 y$

Begin to isolate $y$ by subtracting $34.3$ on both sides of the equation

$2.94 y = - 23.9$

Isolate y by dividing $2.94$ on both sides of the equation

$y = - 8.13$

Now, we have solved for one of the variables. The next thing to do is plug $y$ into another equation that contains $y$ in it. An easy one to use would be $x = 175 + 15 y$ because $x$ is already isolated

So, plug $y = - 8.13$ into $x = 175 + 15 y$

$x = 175 + 15 \left(- 8.13\right)$

Distribute $15$ throughout the set of parenthesis

$x = 175 - 121.95$

Subtract

$x = 53.05$

And now we have solved for $y$ and $x$. The only variable left is $z$

To solve for $z$, you have to plug $y = - 8.13$ into the equation

$z = 10 \left(- 8.13\right)$

Multiply

$z = - 81.3$

$x = 53.05$
$y = - 8.13$
$z = - 81.3$