2007-08-07 10:12:03 · 5 answers · asked by Jessica W 1 in Science & Mathematics ➔ Mathematics
Hey there!
An equation has no solution when the answer doesn't satisfy the equation, or when the solution is a false statement.
False statements include 5=3, 0=2, 1=9 etc.
An equation has no solution even when dividing by 0.
For example: 4/0=x
The answer is infinity, but if we multiply both sides of the equation by 0, it would be 4=0, which is false.
No solutions can also occur when the solution is not real.
sqrt(-1)=x
The answer is i, but i is not a real number, therefore there is no solution.
This has no solution.
sqrt(x)=-1 -->
x=(-1)^2 -->
x=1
sqrt(1)=-1 -->
1=-1, false.
No solutions can also occur, in systems of two or more linear equations where the lines are parallel. No solutions also occur in systems of nonlinear equations, where the graphs do not intersect.
Hope it helps!
2007-08-07 11:19:07 · answer #1 · answered by ? 6 · 0⤊ 0⤋
Actually, there are many things that can cause an equation to have no solution. But, by definition, when no real number can satisfy the conditions of the original equation, then it has no solution. The previous posters have identified two instances when this would be true, but many extraneous solutions (results of correct algebraic calculation) will not satisfy the original equation and therefore lead to "no solution" ends.
Ex. sqrt (x) = -4 if we square both sides the problem becomes
x = 16 which is not an acceptable solution for the given equation since we can only accept the primary (positive) square root of the radicand.
2007-08-07 17:24:20 · answer #2 · answered by gfulton57 4 · 0⤊ 0⤋
When an error free solving process leads to something impossible. For example:
x = x + 1
0 = 1
or
x² + 4 = 1
x² = -3 (when you're limited to real numbers)
Any solution that when plugged back in would have you dividing by 0 or taking the log of something negative, and so on.
2007-08-07 17:21:40 · answer #3 · answered by Philo 7 · 0⤊ 0⤋
there are different ways, depending on the equation.
For example, (2X+4)/0 has no solution, because you can`t divide by zero.. or if the sentence is obviously wrong.
Like 35=0 because obviously, 35 doesn't equal 0.
2007-08-07 17:16:10 · answer #4 · answered by Anonymous · 0⤊ 0⤋
The most likely way is when you get down to a contradiction like
2=7 (or any two numbers that are not equal)
0x=5 (which is not possible)
2007-08-07 17:16:05 · answer #5 · answered by Amy W 6 · 1⤊ 0⤋