Question 1023591: I need to solve system by graphing, then find the point of intersection:
y=x+5
y=-x+3
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Each equation will be graphed as a straight line.
Once they are graphed, the apparent intersection point will be located,
and its coordinates are the apparent solution to the problem.
Usually those values need to be verified, because sometimes appearances are deceiving.
I will show how to graph each line separately first for clarity.
The line represented by  has
a slope of  (the coefficient of x), ans
a y-intercept of  (meaning that (0,5) is the point where the line crosses the y-axis.
Based on that information, we graph the line as
 , starting from (0,5), and moving from point to point to (1,6), (2,7),
by increasing y by as x increases by 1 (one square to thew left and one up),
and also to (-1,4), (-2,3), (-3,2), (-4,1), and (-5,0),
moving the opposite way, one square to the left and one down each time.
The line represented by  has
a slope of  (the coefficient of x), ans
a y-intercept of  (meaning that (0,3) is the point where the line crosses the y-axis.
Based on that information, we graph the line as
 , starting from (0,3), and moving from point to point to (1,2), (2,1), (3,0), (4,-1), and (5,-2),
by increasing y by as x increases by 1 (one square to the right and one down each time),
and also to (-1,4), and (-2,5),
moving the opposite way, one square to the left and one up each time.
A graph with the two lines together looks like this
 The lines appear to intersect at (-1,4), with  ,
and we know that (-1,4) was a point we went through as we drew each line,
so verification seems pointless in this case.
However, verification may still be expected,
and it would be needed if we had drawn the lines some other way.
Substituting  we get
 and  ,
which verifies solution .
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