# How do you solve the following linear system: 3x-2y=7, 3x+4y=12?

Nov 12, 2015

The solution for the system of equations is :
color(blue)(y=5/6

color(blue)(x=(26)/(9)

#### Explanation:

color(blue)(3x)−2y=7......equation $1$
$\textcolor{b l u e}{3 x} + 4 y = 12$......equation $2$

We can solve the system of equations by elimination

By subtracting equation $2$ from $1$ we can eliminate color(blue)(3x

cancelcolor(blue)(3x)−2y=7
$- \cancel{\textcolor{b l u e}{3 x}} - 4 y = - 12$

$- 6 y = - 5$

$y = \frac{- 5}{- 6}$

color(blue)(y=5/6

Now we substitute this value of $y$ in equation $1$ to find $x$:

3x−2y=7

$3 x = 7 + 2 y$

3x=7+cancel2*color(blue)(5/cancel6

$3 x = 7 + \frac{5}{3}$

$3 x = \frac{21 + 5}{3}$

$3 x = \frac{26}{3}$

$x = \frac{26}{3 \cdot 3}$

color(blue)(x=(26)/(9)