# How do determine if #x+y=-2,y=x+2# has no solution, one solution, or an Infinite number of solutions and find the solution?

##### 1 Answer

There is a single solution. As an

#### Explanation:

There are a few things we can do to determine if the system is inconsistent (has no solutions) or is consistent (has one or many solutions). The easiest, in this case, is to eliminate a variable and see if the remaining equation can ever be true.

Consider that our second equation is

We now have two expressions for

Remember that