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+2y=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)

Related questions
See all questions in Systems Using Substitution
Impact of this question
10016 views around the world
You can reuse this answer
Creative Commons License