# How do you solve the system x+2y=13 and -2x-3y=-18 using substitution?

May 29, 2017

$x = - 3$ and $y = 8$

#### Explanation:

Starting with $x + 2 y = 13$, get $x$ by itself on the left-hand side by subtracting $2 y$ from both sides.

$x = - 2 y + 13$

This gives us a new name for $x$, which we can plug back in to

$- 2 \textcolor{red}{x} - 3 y = - 18$

$- 2 \left(\textcolor{red}{- 2 y + 13}\right) - 3 y = - 18$

$4 y - 26 - 3 y = - 18$

Combine the terms with $y$

$y - 26 = - 18$

Add $26$ to both sides.

$y = 8$

Now plug $y = 8$ back into one of the two equations with both $x$ and $y$ still in it from above.

$x = - 2 \textcolor{red}{y} + 13$

$x = - 2 \left(\textcolor{red}{8}\right) + 13$

$x = - 16 + 13$

$x = - 3$

ANSWER: $x = - 3$ and $y = 8$

May 29, 2017

$x = - 3$

$y = 8$

#### Explanation:

Since,

$x + 2 y = 13$

Then,

$x = 13 - 2 y$

Substuting $\left[x = 13 - 2 y\right]$ in the other equation, $\left(- 2 x - 3 y = - 1\right)$, It becomes

$- 2 \left(13 - 2 y\right) - 3 y = - 18$

Simplify,

$- 26 + 4 y - 3 y = - 18$

Which is the same as:

$- 26 + y = - 18$

Put $y$ on the left side of the equal sign and actual numbers on the right

$y = - 18 + 26$

$y = 8$

Go back and solve $\left[x = 13 - 2 y\right]$ for $x$, since you now know what $y$ is:

$x = 13 - 2 \left(8\right)$

$x = 13 - 16$

$x = - 3$

Ta da! Please do correct if I'm wrong...
Cheers and all the best!