Question: What Are Infinitely Many Solutions?

What happens when everything cancels out in a system of equations?

1 Expert Answer If both x and y are going to cancel out, then you have either no solution or infinitely many solutions.

If the constant on the right are going to cancel out (same number with opposite signs) then there are infinitely many solutions (same line)..

Does empty set mean no solution?

If an equation has no solutions, its solution set is the empty set or null set–a set with no members, denoted Ø. For example, the solution set to x2 = – 9 is Ø, because no number, when squared, is equal to a negative number. Sometimes we will be given a set of values from which to find a solution–a replacement set.

Which equation has no solution 4x 2 =- 6?

Answer: Option A) |4x – 2| = – 6 has no solution. Since left hand side of function is in modulus, so it will always gives positive values but right hand side is – 6 , So, there are no values of x that make the equation true.

What is an example of one solution?

This is the normal case, as in our example where the equation 2x + 3 = 7 had exactly one solution, namely x = 2.

How do you know if a solution is unique?

A nxn homogeneous system of linear equations has a unique solution (the trivial solution) if and only if its determinant is non-zero. If this determinant is zero, then the system has an infinite number of solutions.

What if the limit is 0 0?

Typically, zero in the denominator means it’s undefined. … When simply evaluating an equation 0/0 is undefined. However, in take the limit, if we get 0/0 we can get a variety of answers and the only way to know which on is correct is to actually compute the limit.

How do you know if a system has infinitely many solutions?

A system of linear equations has no solution when the graphs are parallel. Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line. Want to learn more about the number of solutions to systems of equations?

What is the condition of no solution?

If there are infinitely many solutions of the given pair of linear equations, the equations are called dependent (consistent). If the lines are parallel, there is no solution for the pair of linear equations. If there is no solution of the given pair of linear equations, the equations are called inconsistent.

What does X R mean?

19. When we say that x∈R, we mean that x is simply a (one-dimensional) scalar that happens to be a real number. For example, we might have x=−2 or x=42.

What is symbol for no solution?

symbol ØSometimes 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.

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 . … 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.

Do parallel lines have infinitely many solutions?

If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. … When the lines are parallel, there are no solutions, and sometimes the two equations will graph as the same line, in which case we have an infinite number of solutions.

Is no solution inconsistent?

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. 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 the value of 0 by 0?

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.

What is an example of infinitely many solutions?

When a problem has infinite solutions, you’ll end up with a statement that’s true no matter what. For example: 3=3 This is true because we know 3 equals 3, and there’s no variable in sight. Therefore we can conclude that the problem has infinite solutions. You can solve this as you would any other equation.

What is infinitely many solutions in math?

The first is when we have what is called infinite solutions. This happens when all numbers are solutions. This situation means that there is no one solution. … The equation 2x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions.

How do you write an equation with infinitely many solutions?

In this case, the idea is that you have to create something that makes both the right side of the equation and the left side to be equal to each other which gives you an infinite number of solutions. so if you have 5x-8 on the left, you need 5x-8 on the right for everything to cancel and end up with 0=0.

What does 0 0 mean in a equation?

2 Answers. Wataru. . 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.

Does a free variable mean infinitely many solutions?

Theorem 1 (Infinitely Many Solutions) A system of m × n linear homogeneous equations with fewer equations than unknowns (m < n) has at least one free variable, hence an infinite number of solutions. Therefore, such a system always has the zero solution and also a nonzero solution.

What does the R mean in math?

real numbersRecall the notation that R stands for the real numbers.

How do you find 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 tell if a system of equations has no solution or infinitely many?

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.