How do you solve the system 0.3x-0.2y=0.5 and x-2y=-5 using substitution?

1 Answer
Jun 12, 2017

$x = 5$, $y = 5$

Explanation:

Here we have a system of equations:

$0.3 x - 0.2 y = 0.5$
$x - 2 y = - 5$

Let's focus on the second equation and rewrite the equation so that $x$ is in terms of $y$:

$x - 2 y = - 5$

$x = 2 y - 5$

Now, we can substitute this equation for $x$ into the first equation and solve for $y$:

$0.3 \left(2 y - 5\right) - 0.2 y = 0.5$

$0.3 \left(2 y\right) - 0.3 \left(5\right) - 0.2 y = 0.5$

$0.6 y - 1.5 - 0.2 y = 0.5$

$0.6 y - 0.2 y = 0.5 + 1.5$

$0.4 y = 2$

$y = \frac{2}{0.4} = \frac{20}{4} = 5$

Now that we have found $y$, we can (again) substitute it back into the second equation to find $x$:

$x - 2 \left(5\right) = - 5$

$x - 10 = - 5$

$x = 5$

So, our answers are:

$x = 5$ and $y = 5$