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

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Answer 1 · 2018-06-24T20:20:58

See a solution process below:

First, we need to graph each equation by solving each equation for two points and then drawing a straight line through the two points.

Equation 1:

First Point: For #x = 0#

#y = 0 + 2#

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

Second Point: For #x = 2#

#y = 2 + 2#

#y = 4# or #(2, 4)#

graph{(y - x - 2)(x^2+(y-2)^2-0.075)((x-2)^2+(y-4)^2-0.075)=0 [-15, 15, -10, 5]}

Equation 2:

First Point: For #x = 0#

#y = -0 - 3#

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

Second Point: For #x = 3#

#y = -3 - 3#

#y = -6# or #(3, -6)#

graph{(y + x + 3)(y - x - 2)(x^2+(y+3)^2-0.075)((x-3)^2+(y+6)^2-0.075)=0 [-15, 15, -10, 5]}

From the graphs we can see the line intersects at: #(color(red)(-2.5),color(red)(-0.5))#

graph{(y + x + 3)(y - x - 2)((x+2.5)^2+(y+0.5)^2-0.075)=0 [-15, 15, -10, 5]}

By definition: a consistent system has at least one solution

Therefore, this system of equations is consistent