How do you solve the following system?:  2x+3y=11, -x+y=-3

Dec 5, 2015

The solution for the system of equations is
color(blue)(x=4,y=1

Explanation:

$\textcolor{b l u e}{2 x} + 3 y = 11$.....................equation $1$

$- x + y = - 3$ ,multiplying this equation by $2$
$\textcolor{b l u e}{- 2 x} + 2 y = - 6$..............equation $2$

Solving by elimination .

Adding equations $1$and $2$ would result in elimination of the term color(blue)(2x.

$\cancel{\textcolor{b l u e}{2 x}} + 3 y = 11$
$\cancel{\textcolor{b l u e}{- 2 x}} + 2 y = - 6$

$5 y = 5$

$y = \frac{5}{5}$

color(blue)(y=1

Now we substitute the value of $y$ in equation $2$ to find $x$:
$- x + y = - 3$

$y + 3 = x$

$1 + 3 = x$

color(blue)(x=4