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

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #131 : Linear / Rational / Variable Equations

Given the following system, find the solution:

x = y – 2

2x – 2y = 2

Possible Answers:

(1, 1)

(0, 0)

(0, 1)

(1, 2)

no solution

Correct answer:

no solution

Explanation:

When 2 equations in a system have the same slopes, they will either have no solution or infinite solutions. Since the y-intercepts are not the same, there is no solution to this system.

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

Solve for :

Possible Answers:

No solution

Infinite Solutions 

Correct answer:

No solution

Explanation:

Like other "solve for x" problems, to begin it, the goal is to get x by itself on one side of the equals sign. In this problem, before doing so, the imaginary -1 in front of (-27x+27) must be distributed. 

Once this is done, you may start to try to get x by itself.

However, when subtracting 27x from either side and doing the same on the other,  the 27x term cancels out. As a result, the equation becomes:

We know this is an untrue statement because these numbers are 5 spaces away from each other on the number line. The final answer is No Solution

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

Given the following system, find the solution:

Possible Answers:

No solution

Correct answer:

No solution

Explanation:

When two equations have the same slope, they will have either no solution or infinite solutions.  By putting both equations into the form , we get:

and

With the equations in this form, we can see that they have the same slope, but different y-intercepts.  Therefore, there is no solution to this system.

Example Question #133 : Linear / Rational / Variable Equations

Solve the following equation for :

Possible Answers:

No solution

Infinite solutions

Correct answer:

No solution

Explanation:

In order to solve for , we must get  by itself on one side of the equation.

First, we can distribute the  on the left side of the equal sign and the  on the right side.

When we try to get  by itself, the  terms on each side of the equation cancel out, leaving us with:

We know this is an untrue statement, so there is no solution to this equation.

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:

6

3

0

no possible solution

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 #44 : Algebra

Nosol1

Possible Answers:

There is no solution

1

–3

–1/2

3

Correct answer:

There is no solution

Explanation:

Nosol2

Example Question #3 : Equations / Inequalities

  

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 #91 : Linear / Rational / Variable Equations

\frac{x+2}{3}=\frac{x}{3} Solve for .

Possible Answers:

No solutions.

Correct answer:

No solutions.

Explanation:

Cross multiplying leaves , which is not possible.

Example Question #1 : 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

III only

II only

II and III 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

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. 

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