# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent -2x + 4y=8 and 6x + 3y= -9?

Feb 26, 2018

See a solution process below:

#### Explanation:

We can find two points for each equation, plot the two points and draw a straight line through the two points.

For Equation: $- 2 x + 4 y = 8$

• First Point: For $x = 0$

$\left(- 2 \cdot 0\right) + 4 y = 8$

$0 + 4 y = 8$

$4 y = 8$

$\frac{4 y}{\textcolor{red}{4}} = \frac{8}{\textcolor{red}{4}}$

$y = 2$ or $\left(0 , 2\right)$

Second Point: For $y = 0$

$- 2 x + \left(4 \cdot 0\right) = 8$

$- 2 x + 0 = 8$

$- 2 x = 8$

$\frac{- 2 x}{\textcolor{red}{- 2}} = \frac{8}{\textcolor{red}{- 2}}$

$x = - 4$ or $\left(- 4 , 0\right)$

We can next plot the two points on the coordinate plane and draw the straight line through them for the first equation:

graph{(4y - 2x - 8)(x^2+(y-2)^2-0.025)((x+4)^2+y^2-0.025)=0 [-10, 10, -5, 5]}

For Equation: $6 x + 3 y = - 9$

• First Point: For $x = 0$

$\left(6 \cdot 0\right) + 3 y = - 9$

$0 + 3 y = - 9$

$3 y = - 9$

$\frac{3 y}{\textcolor{red}{3}} = - \frac{9}{\textcolor{red}{3}}$

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

Second Point: For $y = 3$

$6 x + \left(3 \cdot 3\right) = - 9$

$6 x + 9 = - 9$

$6 x + 9 - \textcolor{red}{9} = - 9 - \textcolor{red}{9}$

$6 x - 0 = - 18$

$6 x = - 18$

$\frac{6 x}{\textcolor{red}{6}} = - \frac{18}{\textcolor{red}{6}}$

$x = - 3$ or $\left(- 3 , 3\right)$

We can next plot the two points on the coordinate plane and draw the straight line through them for the first equation:

graph{(6x + 3y + 9)(4y - 2x - 8)(x^2+(y+3)^2-0.025)((x+3)^2+(y-3)^2-0.025)=0 [-10, 10, -5, 5]}

We can see these two lines intersect at point: $\left(- 2 , 1\right)$

graph{(6x + 3y + 9)(4y - 2x - 8)((x+2)^2+(y-1)^2-0.015)=0 [-10, 2, -1, 5]}

Because there is at least one solution to this system of equations it is by definition consistent.