What is the definition of no solution
The Correct Answer and Explanation is:
The term “no solution” refers to a situation in mathematics where an equation or system of equations does not have any possible values for the variables that can satisfy the equation. In simpler terms, it means that the equation cannot be true for any value of the unknowns involved.
For example, consider the linear equation:
2x+3=2x+52x + 3 = 2x + 52x+3=2x+5
If we attempt to solve for xxx, we would subtract 2x2x2x from both sides, which simplifies to:
3=53 = 53=5
Since 333 is never equal to 555, this equation has no solution. There is no value of xxx that can make this equation true. In this case, the system is inconsistent, meaning there is no set of values that satisfy the equation.
Another example could involve a system of equations. For instance: x+y=4(Equation 1)x + y = 4 \quad \text{(Equation 1)}x+y=4(Equation 1) x+y=6(Equation 2)x + y = 6 \quad \text{(Equation 2)}x+y=6(Equation 2)
If we attempt to solve this system, we see that the two equations describe parallel lines on a graph. Parallel lines never intersect, meaning there is no point where both equations are satisfied simultaneously. Thus, the system has no solution.
The concept of “no solution” can also appear in quadratic equations or other higher-degree equations. It typically indicates a contradiction in the values or relationships expressed in the equation or system. Mathematically, it can be represented using a null set, symbolized by ∅\emptyset∅, showing that no solutions exist within the set of real numbers, complex numbers, or any other specified number system.
In conclusion, “no solution” occurs when an equation, system of equations, or mathematical expression has no possible solutions or values that satisfy the given conditions.
