How do you solve the following system?:  x - 3y = 0 , 3x + y = 7

May 3, 2018

$x = \frac{21}{10}$ and $y = \frac{7}{10}$

Explanation:

$x - 3 y = 0$
$3 x + y = 7$

Let's solve for $x$ in the first equation so we can use substitution

$x = 3 y$

Now plug that into the second equation

$3 \left(3 y\right) + y = 7$

$9 y + y = 7$

$10 y = 7$

$y = \frac{7}{10}$

Plug that back into the first equation:

$x = 3 \left(\frac{7}{10}\right)$

$x = \frac{21}{10}$

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To check our work, let's substitute $\frac{21}{10}$ and $\frac{7}{10}$ for $x$ and $y$ and solve. If we get the same answer as the equation, we are correct

$3 x + y = 7$

$3 \left(\frac{21}{10}\right) + \left(\frac{7}{10}\right)$ should equal $7$

$\frac{63}{10} + \frac{7}{10}$

$\frac{70}{10}$

$7$ equals $7$

We were right!