Question

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

Answer 1

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`

Answer 2

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.