# 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#?

##### 1 Answer

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:**

**First Point:**For#x = 0#

**Second Point:** For

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:**

**First Point:**For#x = 0#

**Second Point:** For

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:

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**.