# How do you solve the system y= 1.2x - 46 and y = 0.6x - 0.22 by substitution?

May 19, 2015

Choose one equation to solve for one of the variables in terms of the other variable (your choice). Substitute the solution you get into the other equation.

$y = 1.2 x - 46$
$y = 0.6 x - 0 , 22$

I choose to solve the first equation for $y$ in terms of $x$ (because it is already solved for $y$ in terms of $x$!)
$y = 1.2 x - 46$

Now replace any $y$'s in the second equation with $1.2 x - 46$

We get:

$1.2 x - 46 = 0.6 x - 0.22$

Solve for $x$.

$1.2 x - 0.6 x = 46 - 0.22$

$0.6 x = 45.78$

$x = \frac{45.78}{0.6}$ (if you have a calculator, you can use it)

$x = \frac{45.78}{0.6} = \frac{45.78}{\frac{6}{10}} = 45.78 \cdot \left(\frac{10}{6}\right) = \frac{457.8}{6} = 76.3$

Finally, finish by finding $y$.
We already "solved" the first equation for $y$ in terms of $x$
$y = 1.2 x - 46$.

So in the solution, $y = 1.2 \left(76.3\right) - 46 = 45.56$

The solution is:

$x = 76.3$ and $y = 45.56$.