# How do you solve the system x+3y=-4 and 2x+6y=5 using substitution?

Oct 16, 2016

This systen has no solutions. See explanation for details.

#### Explanation:

The original system is:

$\left\{\begin{matrix}x + 3 y = - 4 \\ 2 x + 6 y = 5\end{matrix}\right.$

To solve it using substitution we have to calculate one of the variables from one equation to substitute it in the other. We can easily calculate $x$ from the first equation:

$x = - 4 - 3 y$

Now we put the value to the second equation:

$2 \left(- 4 - 3 y\right) + 6 y = 5$

If we try to calculate $y$ from this equation we get:

$- 8 - 6 y + 6 y = 5$

If we reduce like terms we get:

$- 8 = 5$

This equality is of course false which means that the original system has no solutions.