If an equation has no solutions, we write … for the solution set. … means the null set (or empty set). Sometimes, you may be given a replacement set, and asked to test whether the equation is true for all values in the replacement set.

What symbols mean infinite solutions?

Sometimes we use the symbol ∞, which means infinity, to represent infinite solutions.

What is the symbol for no solution?

Sometimes we use the symbol Ø to represent no solutions. That symbol means “empty set” which means that the set of all answers is empty. In other words, there is no answer.

What equations have no solution?

If the variable terms are the same and the constant terms are different, then the equation has no solutions. So, the constant terms are different. This means the equation has no solutions if the variable terms are the same.

What indicates no solution?

If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

What is an example of no solution?

A system has no solution if the equations are inconsistent, they are contradictory. for example 2x+3y=10, 2x+3y=12 has no solution. is the rref form of the matrix for this system. … The row of 0’s only means that one of the original equations was redundant. The solution set would be exactly the same if it were removed.

What does the R mean in math?

In maths, the letter R denotes the set of all real numbers. … In other words, real numbers are defined as the points on an infinitely extended line. This line is called the number line or the real line, on which the points of integers are evenly ranged.

How do you identify a unique solution?

In a set of linear simultaneous equations, a unique solution exists if and only if, (a) the number of unknowns and the number of equations are equal, (b) all equations are consistent, and (c) there is no linear dependence between any two or more equations, that is, all equations are independent.

How do you know if there is no solution or infinite solutions?

No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.

Is 0 0 infinite or no solution?

For an answer to have an infinite solution, the two equations when you solve will equal 0=0 . Here is a problem that has an infinite number of solutions. If you solve this your answer would be 0=0 this means the problem has an infinite number of solutions.

How do you know if two equations have no solution?

The coefficients are the numbers alongside the variables. The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

How do you check if an equation has no solution?

When a problem has no solution you’ll end up with a statement that’s false. For example: 0=1 This is false because we know zero can’t equal one. Therefore we can conclude that the problem has no solution.

What does infinite solution look like?

An infinite solution has both sides equal. For example, 6x + 2y ” 8 = 12x +4y ” 16. If you simplify the equation using an infinite solutions formula or method, you’ll get both sides equal, hence, it is an infinite solution.

How do you know if there are infinitely many solutions?

An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

What determinant has no solution?

If the determinant of a matrix is zero, then the linear system of equations it represents has no solution. In other words, the system of equations contains at least two equations that are not linearly independent.

When two lines are parallel the system has an infinite number of solutions?

Infinite Solutions: Sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions. No Solution: When the lines that make up a system are parallel, there are no solutions because the two lines share no points in common.