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

Question

4933 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-12T07:50:21

$x = 5$ $x=5$ , $y = 5$ $y=5$

Here we have a system of equations:

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

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

$x - 2 y = - 5$ $x-2y=-5$

$x = 2 y - 5$ $x=2y-5$

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

$0.3 (2 y - 5) - 0.2 y = 0.5$ $0.3(2y-5)-0.2y=0.5$

$0.3 (2 y) - 0.3 (5) - 0.2 y = 0.5$ $0.3(2y)-0.3(5)-0.2y=0.5$

$0.6 y - 1.5 - 0.2 y = 0.5$ $0.6y-1.5-0.2y=0.5$

$0.6 y - 0.2 y = 0.5 + 1.5$ $0.6y-0.2y=0.5+1.5$

$0.4 y = 2$ $0.4y=2$

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

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

$x - 2 (5) = - 5$ $x-2(5)=-5$

$x - 10 = - 5$ $x-10=-5$

$x = 5$ $x=5$

So, our answers are:

$x = 5$ $x=5$ and $y = 5$ $y=5$

How do you solve the system 0.3x-0.2y=0.50.3x−0.2y=0.50.3x-0.2y=0.5 and x-2y=-5x−2y=−5x-2y=-5 using substitution?