For linear equations,
- if in your solution, the variable drops out, and you end up with a true statement, there will be an infinite number of solutions.
e.g. 3x - 9 = 3(x-3)
solving you get 0 = 0, which is true, so infinite number
- if in your solution, the variable drops out, and you end up with a false statement, there will be no solution
e.g. 3x - 8 = 3(x-3)
solving you get -8 = -9, which is false, so no solution.
For higher level equations, such as quadratics, cubic, log equations, etc
let y = (the expression forming your equation) and graph it. If it does not cross the x-axis, there will be no solution.
e.g. x^4 + x + 29 = 0
let y = x^4 + x + 29
http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E4+%2B+x+%2B+29
graph does not cross the x-axis, thus, no real number solution
3. Explain how you can tell if an equation has no infinite solution, write an example and solve.
I don't understand how you can tell, help?
1 answer
1 answer