Question: When Can An Equation Have Infinite Solutions?

What happens when an equation is 0 0?

2 Answers.

If you end with 0=0 , then it means that the left-hand side and the right-hand side of the equation are equal to each other regardless of the values of the variables involved; therefore, its solution set is all real numbers for each variable..

What is the value of 0 by 0?

Again, any number multiplied by 0 is 0 and so this time every number solves the equation instead of there being a single number that can be taken as the value of 0/0. In general, a single value can’t be assigned to a fraction where the denominator is 0 so the value remains undefined.

What does it mean when zero equals zero?

0/0 is undefined. If substituting a value into an expression gives 0/0, there is a chance that the expression has an actual finite value, but it is undefined by this method. We use limits (calculus) to determine this finite value.

How do you know if an equation has one solution no solution or infinite solutions?

Explanation: When finding how many solutions an equation has you need to look at the constants and coefficients. The coefficients are the numbers alongside the variables. … If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

What is an example of no solution?

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. … This is because there is truly no solution—there are no values for x that will make the equation 12 + 2x – 8 = 7x + 5 – 5x true.

What does infinite solutions 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.

At what condition is the pair of equations Ax 2y 7 and 3x by 16?

The pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines if. a = b. 3a = 2b.

How do you know if an equation has infinite solutions?

If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.

What makes an infinite solution?

Infinite solutions would mean that any value for the variable would make the equation true. Let’s look at the following equation: Note that we have variables on both sides of the equation. So we’ll subtract from both sides to eliminate the on the right side of the equation.

What is the formula for no solution?

Case 2. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. This type of equation is called an inconsistent pair of linear equations.

How do you know if a system has no solution?

A system has no solutions if the lines are parallel. When solving the system, if you get a false statement (a number equal to a different number) this means there are no solutions.

What is the solution of given pair of equations?

For a given pair of linear equations in two variables, the graph is represented by two lines. If the lines intersect at a point, that point gives the unique solution for the two equations. If there is a unique solution of the given pair of equations, the equations are called consistent.

Is 0 a free variable?

zero free variables are present. This is identical to requiring that the number n of variables equal the number of lead variables, or rank = n.

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.

What lines have infinite solutions?

A system of linear equations has infinite solutions when the graphs are the exact same line.

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