How do you solve the system of equations by graphing #y=5x-2, y=-2x+5#?

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Answer 1 · 2017-11-07T03:46:22

#x=1, y=3#

#y=5x-2# [A]
#y=-2x+5# [B]

Both [A] and [B] are equations of straight lines.

[A] has a slope of +5 and y-intercept of -2

[B] has a slope of -2 and y-intercept of +5

The solution of the system occurs at the intersection of the lines.

As shown below:

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

The intersection occurs at the point #(1, 3)#

Hence, the solution of the system is: #x=1, y=3#