# How do you solve 3x+y=16 and 2x+y=11?

Jun 30, 2015

The solutions are:
color(blue)(x=5
 color(blue)(y = 1

#### Explanation:

$3 x + \textcolor{g r e e n}{y} = 16$ ........equation $\left(1\right)$

$2 x + \textcolor{g r e e n}{y} = 11$..........equation $\left(2\right)$

These equations can be solved through elimination :
(by eliminating color(green)(y)

Subtracting equation $\left(2\right)$ from equation $\left(1\right)$ :

$3 x + \cancel{\textcolor{g r e e n}{y}} = 16$

$- 2 x - \cancel{\textcolor{g r e e n}{y}} = - 11$

color(blue)(x=5

Now , finding $y$, from equation $1$ :

$y = 16 - 3 x$
$= 16 - 3. \left(5\right)$
 color(blue)(y = 1