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

Algebra ->  Coordinate-system -> 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       Log On


   



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) About Me  (Show Source):
You can put this solution on YOUR website!
For each of your problems, solve both of the equations for y. In other words, using the rules for manipulating equations, rearrange both equations in the problem so that each is in the form y+=+mx+%2B+b. Then compare the m and b parts of each equation.

You will have two equations:
y=m%5B1%5Dx%2Bb%5B1%5D and y=m%5B2%5Dx%2Bb%5B2%5D

If m%5B1%5D%3C%3Em%5B2%5D, then your system has exactly one element in the solution set.

If m%5B1%5D=m%5B2%5D AND b%5B1%5D%3C%3Eb%5B2%5D, then your system has an empty solution set.

If m%5B1%5D=m%5B2%5D AND b%5B1%5D=b%5B2%5D, then your system has many elements in the solution set, infinitely many, in fact.