# How do you solve the following system of equations?: 3x-y=7 , 4x+3y=8?

##### 1 Answer
Dec 27, 2015

The solution for the system of equations is

color(blue)(x=29/13, y=-4/13

#### Explanation:

$3 x - y = 7$, multiplying the equation by $3$
$9 x - \textcolor{b l u e}{3 y} = 21$.....equation $\left(1\right)$

$4 x + \textcolor{b l u e}{3 y} = 8$........equation $\left(2\right)$

Solving by elimination

Adding equations $1$ and $2$:

$9 x - \cancel{\textcolor{b l u e}{3 y}} = 21$

$4 x + \cancel{\textcolor{b l u e}{3 y}} = 8$

$13 x = 29$

color(blue)(x=29/13

Now, we find $y$ by substituting $x$ in equation $1$:

$3 x - y = 7$

$3 x - 7 = y$

$3 \times \textcolor{b l u e}{\frac{29}{13}} - 7 = y$

$\frac{87}{13} - 7 = y$

$\frac{87}{13} - \frac{91}{13} = y$

color(blue)(y=-4/13