What is the definition of no solution
The Correct Answer and Explanation is:
In mathematics, the term “no solution” refers to a situation where an equation or a system of equations has no values for the variables that satisfy it. This means that there is no possible value for the unknowns that will make both sides of the equation true. In other words, the equation or system of equations is inconsistent.
For example, consider the equation 2x+5=2x+82x + 5 = 2x + 82x+5=2x+8. If we try to solve for xxx, we first subtract 2x2x2x from both sides, which simplifies to 5=85 = 85=8. Since 5 is not equal to 8, the equation has no solution. This is an example of an inconsistent equation, where no value for xxx will make the equation true. Thus, the equation has no solution.
In the case of a system of linear equations, no solution occurs when the system represents two or more lines that are parallel and do not intersect. For instance, consider the system: y=2x+3y = 2x + 3y=2x+3 y=2x−1y = 2x – 1y=2x−1
Here, both equations represent lines with the same slope (2), but they have different y-intercepts (3 and -1). Since parallel lines never meet, there is no point where both equations are satisfied simultaneously, meaning the system has no solution.
In real-world contexts, no solution can occur when trying to model a scenario that is inherently impossible, such as trying to find a negative number of items in a store or trying to assign an impossible value to a variable, such as dividing by zero. Thus, no solution is a fundamental concept in algebra and other areas of mathematics, indicating that the equation or system is inconsistent and has no set of solutions.
