# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent x + 3y = -3, 2x – y = 8?

Feb 21, 2018

The point of intersection is: $\left(x , y\right) = \left(3 , - 2\right)$
The system is consistent as there is a shared point.

#### Explanation:

Consider $x + 3 y = - 3$

Point ${P}_{1}$ is on the x-axis at $y = 0 \implies x + 0 = - 3$
$\textcolor{w h i t e}{\text{dddddddddddddddddddd}} {P}_{1} \to \left({x}_{1} , {y}_{1}\right) = \left(- 3 , 0\right)$

Point ${P}_{2}$ the y-axis at $x = 0 \implies 3 y = - 3 \implies y = - 1$
$\textcolor{w h i t e}{\text{dddddddddddddddddddd}} {P}_{2} \to \left({x}_{2} , {y}_{2}\right) = \left(0 , - 1\right)$

Draw a strait line through ${P}_{1} \mathmr{and} {P}_{2}$ and continue to the edge of the graphing area.
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Consider $2 x - y = 8$

Point ${P}_{3}$ is on the x-axis at $y = 0 \implies 2 x = 8 \implies x = 4$
$\textcolor{w h i t e}{\text{dddddddddddddddddddd}} {P}_{3} \to \left({x}_{3} , {y}_{3}\right) = \left(4 , 0\right)$

Point ${P}_{4}$ is on the y-axis at $x = 0 \implies - y = 8 \implies y = - 8$
$\textcolor{w h i t e}{\text{dddddddddddddddddddd}} {P}_{4} \to \left({x}_{4.} {y}_{4}\right) = \left(0 , - 8\right)$

Draw a strait line through ${P}_{3} \mathmr{and} {P}_{4}$ and continue to the edge of the graphing area.