# SAT Math : How to find out when an equation has no solution

## Example Questions

### Example Question #1 : How To Find Out When An Equation Has No Solution

Find the solution to the following equation if x = 3:

y = (4x2 - 2)/(9 - x2)

6

3

0

no possible solution

no possible solution

Explanation:

Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.

I.  x = 0

II. x = –1

III. x = 1

II and III only

III only

II only

I only

I, II, and III

I only

Explanation:

### Example Question #3 : Equations / Inequalities

There is no solution

3

–1/2

–3

1

There is no solution

Explanation:

### Example Question #1 : How To Find Out When An Equation Has No Solution

Explanation:

A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.

### Example Question #45 : Algebra

Solve:

Explanation:

First, distribute, making sure to watch for negatives.

Combine like terms.

Subtract 7x from both sides.

### Example Question #2 : How To Find Out When An Equation Has No Solution

Solve:

No Solution

Infinitely Many Solutions

No Solution

Explanation:

First, distribute the  to the terms inside the parentheses.

This is false for any value of . Thus, there is no solution.

### Example Question #5 : Linear / Rational / Variable Equations

Solve .

No solutions

No solutions

Explanation:

By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.

### Example Question #4 : How To Find Out When An Equation Has No Solution

In the above graphic, approximately determine the x values where the graph is neither increasing or decreasing.