Create systems of linear equations with each possible number of solutions.?

Create systems of linear equations with each possible number of solutions.

y=x+3, y=-2x-2; y=x+4, y=x+4; y=2x-6, y=2x+3

Explain the equations, and if there is other ways to write them. Is
it possible for the equations to look completely different but the solution
set still be "infinitely many"?

Meng tian2013-06-22T00:46:50Z

Favorite Answer

y = x + 3
y = -2x - 2
The equations are both linear and the system is consistent, so there is exactly 1 solution.

y = x + 4
y = x + 4
There is only 1 unique equation, and as such, there are infinitely many solutions.

y = 2x - 6
y = 2x + 3
The equations are linear, but the system is inconsistent, so there are no solutions.

It is possible for 2 equations to look different at first glance, yet still have infinitely many solutions. For example, y = x + 4 and 3y = 3x + 12 looks different, but they are essentially the same and will result in infinitely many solutions when put together.