When a true statement such as 0 = 0 results, the equation is an identity, and the solution set is {all real numbers}.
Undefined means there are no solutions possible for the operations in view. The example in question is itself wrong.. n/0 is infinite but not undefined.. 0/0 is undefined.
For an answer to have an infinite solution, the two equations when you solve will equal 0=0 . If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions. For an answer to have no solution both answers would not equal each other. Here is a problem that has no solution.
Since 0 = 0 for any value of x, the system of equations has infinite solutions. Every ordered pair (x, y) which satisfies y = x + 17 (the isolation equation) is a solution to the system. The system is dependent (and consistent). The two equations describe the same line--y = x + 17.
Applying the Principle of Zero Products, you know that if the product is 0, then one or both of the factors has to be 0. Set each factor equal to 0. You can check these solutions by substituting each one at a time into the original equation, (x + 4)(x – 3) = 0. You can also try another number to see what happens.
Since 0 = 0 for any value of x, the system of equations has infinite solutions. Every ordered pair (x, y) which satisfies y = x + 17 (the isolation equation) is a solution to the system.
The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. Also, be careful not to make the mistake of thinking that the equation 4 = 5 means that 4 and 5 are values for x that are solutions.
we obtain 0=0, this means the equation is in fact an identity which is true for all values of x. As an equation, its solution is that x can take any real value (assuming we are supposed to be finding real solutions).
Originally Answered: what is the solution of a system of equations when the third equation states that 0 = 1? There is no solution to a system of equations where any of the equations is 0=1, or any other single equation which has no solution.
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The principal solution for this case will be x = 0, π, 2π as these values satisfy the given equation lying in the interval [0, 2π]. But, we know that if sin x = 0, then x = 0, π, 2π, π, -2π, -6π, etc.
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