# What kind of solutions does #3x + 2y = 4# and #2x - y = 5# have?

##### 2 Answers

Apr 3, 2015

The answer is:

Given:

We need to write one of them in terms of the other one. In this problem the easiest way to do this is using

Now replace

Now we know the value of

So the result is

Apr 3, 2015

The system of equations would have an unique solution.

Slope of 3x+2y =4 is -3/2 and the slope of 2x-y=5 is 2. Since the slopes are different, they are not parallel and would intersect at some point. Hence the solution would be unique.