# How do you solve x + y = 23 and y = x - 5?

Feb 15, 2016

$x = 14 \mathmr{and} y = 9$

#### Explanation:

Since $y = x - 5$ in the second equation, we may substitute this fact into the first equation and then solve for $x$.
Doing so we get :

$x + \left(x - 5\right) = 23$

$\therefore 2 x = 28$

$\therefore x = 14$.

Now back-substitute to get $y = 14 - 5 = 9$.

Feb 15, 2016

The solution for the system of equations is:
color(blue)(x=14

color(blue)(y=9

#### Explanation:

$x + y = 23$.......equation $1$
$x - y = 5$..........equation $2$

Solving by elimination.

Adding equations $1$ and $2$

$x + \cancel{\textcolor{b l u e}{y}} = 23$
$x - \cancel{\textcolor{b l u e}{y}} = 5$

$2 x = 28$

$x = \frac{28}{2}$

color(blue)(x=14

Finding $y$ from equation $1$:
$x + y = 23$

$y = 23 - x$

$y = 23 - 14$

color(blue)(y=9