# How do you determine whether a linear system has one solution, many solutions, or no solution when given 3x - y = -6 and x + y = 2?

##### 1 Answer

One solution, (-1,3)

#### Explanation:

Although there are multiple ways one could solve this, I will begin with the algerbraic path to finding this solution. (Skip to bottom for shortcut)

We begin with two equations...

Lets first put them into

1)

2)

3)

4)

Now the second equation

1)

2)

Now that both are in y=mx+b format, set the equations equal to eachother.

Then solve for x.....

However there is a faster way to do this... using the process of elimination...

*_**_*** _**____ Add these equations together

4x=-4

x=-1

Then subsitute the x=-1 into any of the other equations to find the y value....