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#?

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

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

• First Point: For #x = 0#

#(-2 * 0) + 4y = 8#

#0 + 4y = 8#

#4y = 8#

#(4y)/color(red)(4) = 8/color(red)(4)#

#y = 2# or #(0, 2)#

Second Point: For #y = 0#

#-2x + (4 * 0) = 8#

#-2x + 0 = 8#

#-2x = 8#

#(-2x)/color(red)(-2) = 8/color(red)(-2)#

#x = -4# or #(-4, 0)#

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: #6x + 3y = -9#

• First Point: For #x = 0#

#(6 * 0) + 3y = -9#

#0 + 3y = -9#

#3y = -9#

#(3y)/color(red)(3) = -9/color(red)(3)#

#y = -3# or #(0, -3)#

Second Point: For #y = 3#

#6x + (3 * 3) = -9#

#6x + 9 = -9#

#6x + 9 - color(red)(9) = -9 - color(red)(9)#

#6x - 0 = -18#

#6x = -18#

#(6x)/color(red)(6) = -18/color(red)(6)#

#x = -3# or #(-3, 3)#

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: #(-2, 1)#

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.