How do you solve the following systems of equations by graphing given #y=x-4#, #2y=-x+10#?

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Answer 1 · 2018-06-24T12:22:08

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 - 4#

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

Second Point: For #x = 4#

#y = 4 - 4#

#y = 0# or #(4, 0)#

graph{(y - x + 4)(x^2+(y+4)^2-0.075)((x-4)^2+y^2-0.075)=0 [-10, 20, -6, 9]}

Equation 2:

First Point: For #x = 0#

#2y = -0 + 10#

#2y = 10#

#(2y)/color(red)(2) = 10/color(red)(2)#

#y = 5# or #(0, 5)#

Second Point: For #x = 10#

#2y = -10 + 10#

#2y = 0#

#(2y)/color(red)(2) = 0/color(red)(2)#

#y = 0# or #(10,0)#

graph{(2y + x - 10)(y - x + 4)(x^2+(y-5)^2-0.075)((x-10)^2+y^2-0.075)=0 [-10, 20, -6, 9]}

From the graphs we can see the line intersects at: #(color(red)(6),color(red)(2))#

graph{(2y + x - 10)(y - x + 4)((x-6)^2+(y-2)^2-0.075) = 0 [-10, 20, -6, 9]}