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

Study concepts, example questions & explanations for SAT Math

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)

Possible Answers:

no possible solution

6

3

0

Correct answer:

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.

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

Undefined_denom3

 

I.  x = 0

II. x = –1

III. x = 1

Possible Answers:

I only

II and III only

III only

II only

I, II, and III

Correct answer:

I only

Explanation:

 Undefined_denom2

Example Question #3 : How To Find Out When An Equation Has No Solution

Nosol1

Possible Answers:

1

3

–3

There is no solution

–1/2

Correct answer:

There is no solution

Explanation:

Nosol2

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

  

Possible Answers:

None of the other answers

Correct answer:

Explanation:

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

Example Question #5 : How To Find Out When An Equation Has No Solution

Solve: 

Possible Answers:

Correct answer:

Explanation:

First, distribute, making sure to watch for negatives. 

Combine like terms. 

Subtract 7x from both sides. 

Add 18 on both sides and be careful adding integers. 

Example Question #6 : How To Find Out When An Equation Has No Solution

Solve: 

Possible Answers:

No Solution 

Infinitely Many Solutions 

Correct answer:

No Solution 

Explanation:

First, distribute the  to the terms inside the parentheses.

Add 6x to both sides. 

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

Example Question #7 : How To Find Out When An Equation Has No Solution

Solve .

Possible Answers:

No solutions

Correct answer:

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.

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