How do you solve the following linear system: 3x-2y=3 , -x+y=1 ?

Jan 3, 2016

The solution for the system of equations is

color(blue)(x=5,y=6

Explanation:

$\textcolor{b l u e}{3 x} - 2 y = 3$.....equation $\left(1\right)$

$- x + y = 1$, multiplying by $3$,
$- \textcolor{b l u e}{3 x} + 3 y = 3$.....equation $\left(2\right)$

Solving by elimination.

Subtracting equation $2$ from $1$

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

color(blue)(y=6

Finding $x$ from equation $1$:
$3 x - 2 y = 3$

$3 x = 3 + 2 y$

$3 x = 3 + 2 \times 6$

$3 x = 3 + 12$

$3 x = 15$

$x = \frac{15}{3}$

color(blue)(x=5