# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 3x-y=9 and 2x+y=6?

Jan 8, 2018

$\left(3 , 0\right)$

#### Explanation:

Given -

$3 x - y = 9$ -------------(1)
$2 x + y = 6$ -------------(2)

If the slopes are different, both are consistent, else inconsistent.

When the equations are in the form

$a x + b y = c$
The formula for slope is $m = - \frac{a}{b}$
Slope of the first line ${m}_{1} = - \frac{3}{- 1} = 3$
Slope of the second line ${m}_{2} = - \frac{2}{1} = 2$

The slopes are different. They are consistent.

We have to find the intercepts for the two lines to graph them

y-intercept of the 1st line

$3 \left(0\right) - y = 9$
$y = - 9$
$\left(0 , - 9\right)$

x-intercept of the 1st line

$3 x - \left(0\right) = 9$
$x = \frac{9}{3} = 3$
$\left(3 , 0\right)$

y-intercept of the 2nd line

$2 \left(0\right) + y = 6$
$y = 6$
$\left(0 , 6\right)$

x-intercept of the 2nd line

$2 x + 0 = 6$
$x = \frac{6}{2} = 3$
$\left(3 , 0\right)$

[$\left(3 , 0\right)$ is a common point for both the lines. Hence it is the solution]