IXL - Find the number of solutions to a linear equation (Algebra 1 practice)

How many solutions does this equation have?

^–3b + 6b = 3b

no solution

one solution

infinitely many solutions

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Learn with an example

question

How many solutions does this equation have?

2q − 8 = 3q

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 q.

2q − 8

Subtract 2q from both sides

^–8

Subtract 2q from both sides

The statement ^–8 = q is true for one value of q, –8. So, the equation has one solution.

Looking for more? Try these:

Lesson: Equations with infinitely many or no solutions

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Teacher tools

Work it out

Not feeling ready yet? These can help:

C.12Solve linear equations with variables on both sides

C.3Which x satisfies an equation?

Lesson: Equations with infinitely many or no solutions

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