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?
There is a single solution. As an
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