# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 5x - y = -9 and y + 2x = 2?

#### Answer:

$x = - 1$
$y = 4$

#### Explanation:

Determine the intercepts then connect the points to draw the lines.
For $5 x - y = - 9$
When $x = 0$, $y = 9$
$\left(0 , 9\right)$ is point on the line $5 x - y = - 9$

When $y = 0$, $x = - \frac{9}{5}$
$\left(- \frac{9}{5} , 0\right)$ is a point on the line $5 x - y = - 9$

Draw the line passing thru $\left(0 , 9\right)$ and $\left(- \frac{9}{5} , 0\right)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~
For $2 x + y = 2$
When $x = 0$, $y = 2$
$\left(0 , 2\right)$ is point on the line $2 x + y = 2$

When $y = 0$, $x = 1$
$\left(1 , 0\right)$ is a point on the line $2 x + y = 2$

Draw the line passing thru $\left(0 , 2\right)$ and $\left(1 , 0\right)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~
The two lines intersect at $\left(- 1 , 4\right)$

The system is consistent.

Kindly see the graphs

God bless....I hope the explanation is useful.