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

##### 1 Answer

As Realyn has said the point of intersection is

"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:

The simplest thing to do is to convert each of these expressions into the form

So

and

Since both right-hand sides are equal to x, we have:

Adding

We can then insert this back into one of our equations for x (it doesn't matter which), for example

Therefore

And we have the solution: