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#?

1 Answer
Feb 21, 2018

Answer:

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

Explanation:

Consider #x+3y=-3#

Point #P_1# is on the x-axis at #y=0 => x+0=-3#
#color(white)("dddddddddddddddddddd")P_1->(x_1,y_1)=(-3,0)#

Point #P_2# the y-axis at #x=0 => 3y=-3 =>y=-1#
#color(white)("dddddddddddddddddddd")P_2->(x_2,y_2)=(0,-1)#

Draw a strait line through #P_1 and P_2# and continue to the edge of the graphing area.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider #2x-y=8#

Point #P_3# is on the x-axis at #y=0 => 2x=8 => x=4#
#color(white)("dddddddddddddddddddd") P_3->(x_3,y_3)=(4,0)#

Point #P_4# is on the y-axis at #x=0 => -y=8 => y=-8#
#color(white)("dddddddddddddddddddd")P_4->(x_4.y_4)=(0,-8)#

Draw a strait line through #P_3 and P_4# and continue to the edge of the graphing area.
Tony B