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Question 69846: Solve the system by graphing.
x + y = 3
x + y = –1
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! x + y = 3
x + y = –1
This is a "trick" question. Let's convert the two equations to the slope-intercept form:
y=mx+b
In this form the multiplier of x (which is m) is the slope of the graph and b is the value
of y at which the graph crosses the y-axis.
We can convert the top equation to this form by subtracting x from both sides. The
resulting equation is:
y = -x + 3
Compare this equation with the slope-intercept form. Note that the multiplier of x is -1,
so the slope of the graph is -1. The point at which the graph crosses the y-axis
is b which in this case is plus 3.
Now let's re-arrange the second equation into the same slope-intercept form. We do that
by subtracting x from both sides to get:
y = -x - 1
Note that by comparing this equation with the slope-intercept form we again find that
the slope (the multiplier of x) is -1, but this time the point at which the graph
crosses the y-axis (that is the point b) is -1.
What does that tell us? Because the two graphs of these equations have the same slope
they are parallel!!! The only difference is that one line is higher up (crossing the
y-axis at y=3) than the other line (crossing the y-axis at y=-1).
If the pair of equations has a common solution, the two graphs must intersect each other
at that common point. Since the two graphs are parallel in this case, there never
intersect. Therefore, there is no point common to the two graphs. There are no
values
for x and y that will satisfy both equations. Somebody tried to trick you ... or at least
wanted you to think about the situation.
And if you think about it, by looking at the original equations you might have questioned
how in one case x added to y could give you 3 as an answer and in the very next equation
the same value for x added to the same value for y could give you -1 as an answer.
It would have been a clue that something wasn't right.
Hope this helps your understanding of pairs of linear equations.
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