IXL | Find the number of solutions

How many solutions does this equation have?

7y − 5 = 7y

no solution

one solution

infinitely many solutions

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Learn with an example

question

How many solutions does this equation have?

^–m = ^–2m + 5

no solution

one solution

infinitely many solutions

key idea

If solving an equation yields a statement that is false, like 4 = 3, then the equation has no solution.

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution.

If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

solution

Solve for m.

^–m

^–2m + 5

Add 2m to both sides

The statement m = 5 is true for one value of m, 5. So, the equation has one solution.

Looking for more? Try these:

Lesson: Equations with infinitely many or no solutions

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T.1Which x satisfies an equation?

Lesson: Equations with infinitely many or no solutions

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