Find the number of solutions
Key Notes :
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.
Learn with an example
How many solutions does this equation have?
2n − 10n = –8n
- no solution
- one solution
- infinitely many solutions
Solve for n.
2n − 10n = –8n
–8n = –8n Combine like terms
0 = 0 Add 8n to both sides
The statement 0 = 0 is true for every value of n. So, the equation is an identity and has infinitely many solutions.
How many solutions does this equation have?
0 = 2j − 2j
- no solution
- one solution
- infinitely many solutions
Solve for j.
0 = 2j − 2j
0 = 0 Combine like terms
The statement 0 = 0 is true for every value of j. So, the equation is an identity and has infinitely many solutions.
How many solutions does this equation have?
3q = 10 + 3q
- no solution
- one solution
- infinitely many solutions
Solve for q.
3q = 10 + 3q
0 = 10 Subtract 3q from both sides
The statement 0 = 10 is false. So, the equation has no solution.
let’s practice!
