What is the point of intersection of the lines x+2y=4 and -x-3y=-7?

1 Answer
Alan P.
Feb 9, 2015

As Realyn has said the point of intersection is x=-2, y=3

"The point of intersection" of two equations is the point (in this case in the xy-plane) where the lines represented by the two equations intersect; because it is a point on both lines, it is a valid solution pair for both equations. In other words, it is a solution to both equations; in this case it is a solution to both:
x + 2y = 4 and -x - 3y = -7

The simplest thing to do is to convert each of these expressions into the form x = something
So x + 2 y = 4 is re-written as x = 4 - 2y
and
-x - 3y = -7 is re-written as x = 7 - 3y

Since both right-hand sides are equal to x, we have:
4 - 2y = 7 - 3y
Adding (+3y) to both sides and then subtracting 4 from both sides we get:
y = 3

We can then insert this back into one of our equations for x (it doesn't matter which), for example
x = 7 -3y substituting 3 for y gives x = 7 - 3*3 or x = 7 -9
Therefore x = -2

And we have the solution:
(x,y) = (-2,3)

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