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

2 Answers
Apr 3, 2015

The answer is: x=2, y=-1

Given:

1) 2x-y=5

2) 3x+2y=4

We need to write one of them in terms of the other one. In this problem the easiest way to do this is using 1)

y = 2x-5

Now replace y with 2x-5 in 2)

3x+2(2x-5)=4

3x +4x - 10 = 4

7x=14

x =2

Now we know the value of x. So we can plug this value in 1) or 2) to find the value of y. Lets use 1)

2*2-y=5

4-y=5

y=-1

So the result is x=2, y=-1

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.