One Solution, No Solution, Infinite Solution
On the test tomorrow there are three questions that deal with if an equation has one solution, no
solutions, or infinite solutions. Here is a table to help you know what to look for to determine how
many solutions an equation has.
One Solution


If variables are only on
one side then the
equation has only one
solution
If the equation has
variables on both sides
but after each side is
simplified the variables
have different
coefficients then there is
only one solution.

No Solution
Infinite Solutions
If the equation has
variables on both sides
but after each side is
simplified the variables
have the same
coefficients and different
constants then there is
no solution.


If the equation has
variables on both sides
but after each side is
simplified the variables
have the same
coefficients and the
same constants then
there is infinite solutions
If the equation is the
same on both sides then
there is infinite
solutions.
Examples
Examples
Examples
2x + 5 = 7
Variable only on one side
ONE SOLUTION
3x + 7 = 3x + 1
Coefficients are the same,
constants are different!
NO SOLUTION
4x + 8 = 4x + 8
Same on both sides
INFINITE SOLUTIONS
3x + 7 = 2x + 4
Coefficients are different
ONE SOLUTION
4(x + 3) = 2(2x + 12)
Simplify First!!
4x + 12 = 4x + 24
Coefficients are the same,
Constants are different
NO SOLUTION
8x + 12 = 4(2x + 3)
Simplify First!!
8x + 12 = 8x + 12
Same on both sides
INFINITE SOLUTIONS