SOLUTION: For problems1, 2, 3 a. Tell whether the systems of equation have no solution, one solution or many solutions: problem 1

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Question 144638: For problems1, 2, 3
a. Tell whether the systems of equation have no solution, one solution or many solutions:
problem 1 - x+y-1
2x+2y=2
a.

b.
problem 2 - x+y=1
x-y=1
a.
b.
problem 3 - x+y=1
x+y=2
a.
b.
I have tried to solve thee many times, but I seem to come out with different answers each time. Please help me.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!
For each of your problems, solve both of the equations for . In other words, using the rules for manipulating equations, rearrange both equations in the problem so that each is in the form . Then compare the and parts of each equation.

You will have two equations:
and

If , then your system has exactly one element in the solution set.

If AND , then your system has an empty solution set.

If AND , then your system has many elements in the solution set, infinitely many, in fact.

SOLUTION: For problems1, 2, 3 a. Tell whether the systems of equation have no solution, one solution or many solutions: problem 1 - x+y-1 2x+2y=2 a. b. problem 2