Algebra 1 help » Equations / Inequalities » solution of Equations » direct / rational / change Equations » exactly how to discover out once an equation has actually no systems

Solve the reasonable equation:

*


*


*
 or 
*


*


*


Explanation:

With rational equations we must very first note the domain, i beg your pardon is all genuine numbers except

*
 and 
*
. The is, these room the worths of 
*
 that will cause the equation to be undefined. Since the least usual denominator of
*
*
, and 
*
 is 
*
, we deserve to mulitply every term through the LCD come cancel the end the denominators and also reduce the equation to 
*
. Combining favor terms, we finish up with 
*
. Dividing both sides of the equation by the constant, we obtain an answer of 
*
. However, this solution is no in the domain. Thus, over there is NO equipment because 
*
 is an extraneous answer. 


Report one Error

Example concern #2 : exactly how To discover Out once An Equation has actually No solution


Find the solution set:

*

*


Possible Answers:

None of the various other answers.

You are watching: What does it mean if the quadratic equation has no solution


Correct answer:

None of the various other answers.


Explanation:

Use the substitution method to fix for the equipment set.

1) 

*

2) 

*

Solve equation 2 for y:

*

Substitute into equation 1:

*

*

*

If equation 1 was fixed for a variable and also then substituted right into the 2nd equation a similar result would be found. This is due to the fact that these two equations have No solution. Change both equations right into slope-intercept type and graph come visualize. These lines are parallel; they can not intersect. 

*Any an approach of detect the equipment to this device of equations will an outcome in a no equipment answer.


Report an Error

Example question #3 : just how To find Out as soon as An Equation has actually No equipment


How many solutions go the equation below have?

*


Possible Answers:

One


Three


No solutions


Infinite 


Two


Correct answer:

No solutions


Explanation:

When finding how numerous solutions one equation has you must look at the constants and also coefficients.

The coefficients room the numbers alongside the variables.

The constants are the number alone through no variables.

If the coefficients room the exact same on both sides then the sides will not equal, because of this no options will occur.

*

Use distributive home on the appropriate side first.

*

*
*

*

No solutions


Report an Error

Example inquiry #4 : how To uncover Out once An Equation has No equipment


Solve:

*


Possible Answers:
Correct answer:

*


Explanation:

First factorize the numerator.

*

Rewrite the equation.

*

The 

*
 terms have the right to be eliminated.

*

Subtract one top top both sides.

*

However, let"s substitute this answer earlier to the initial equation to check whether if we will get 

*
 as an answer.

*

Simplify the left side.

*

The left next does not fulfill the equation due to the fact that the fraction cannot be divided by zero.

Therefore, 

*
 is no valid.

The prize is:

*


Report one Error

Example question #1 : how To uncover Out as soon as An Equation has actually No solution


Solve for

*
:

*


Possible Answers:

No solution


Correct answer:

No solution


Explanation:

Combine favor terms on each side of the equation:

*

*

Next, subtract 

*
 from both sides. 

*

Then subtract 

*
 from both sides. 

*

*

This is nonsensical; therefore, over there is no equipment to the equation.


Report an Error

Example concern #6 : just how To discover Out once An Equation has actually No equipment


Solve the equation:

*


Possible Answers:

No solution


Correct answer:

No solution


Explanation:

Notice the the end value is a negative. Any an unfavorable or hopeful value the is inside an absolute value sign must an outcome to a hopeful value.

If we separation the equation come its optimistic and negative solutions, we have:

*

*

Solve the very first equation.

*

*

*

The answer to 

*
 is: 
*

Solve the 2nd equation.

*

*

*

The answer to 

*
 is: 
*

If we substitute these 2 solutions back to the initial equation, the results are positive answers and can never ever be same to an adverse one.

The answer is no solution. 


Report an Error
check out Algebra Tutors
Robert Certified guardian
CUNY Medgar Evers College, Bachelor that Science, Computer and also Information Sciences, General.
watch Algebra Tutors
Michael Certified tutor
University of southern California, Bachelor of Science, Finance. The Wharton college UPENN, master in business Administration...

See more: She Says She Needs Space, Here'S What Does It Mean When A Girl Needs Space ?


watch Algebra Tutors
Shana Certified guardian
University of northern Iowa, Bachelor in Arts, Biotechnology. Medical University of southern Carolina, master of Science, Cellul...

All Algebra 1 sources


10 Diagnostic exam 557 practice Tests question of the job Flashcards discover by ide
Popular Subjects
GMAT Tutors in Denver, Calculus Tutors in Chicago, GRE Tutors in Atlanta, plot Tutors in Miami, Chemistry Tutors in san Diego, Physics Tutors in Denver, Spanish Tutors in Los Angeles, reading Tutors in Boston, Algebra Tutors in Chicago, analysis Tutors in Seattle
Popular process & Classes
Spanish courses & classes in san Diego, ISEE process & great in brand-new York City, MCAT courses & classes in Chicago, SSAT courses & great in Houston, ISEE process & great in Denver, ACT process & class in Atlanta, MCAT process & class in Seattle, MCAT process & classes in Atlanta, SAT process & great in Denver, SSAT courses & classes in mountain Francisco-Bay Area
Popular test Prep
LSAT test Prep in Los Angeles, satellite Test prepare in Seattle, GRE test Prep in brand-new York City, LSAT test Prep in Dallas fort Worth, SSAT test Prep in Atlanta, GRE check Prep in Miami, ACT check Prep in san Diego, GMAT check Prep in Boston, satellite Test prep in Miami, MCAT check Prep in Miami
Report an concern with this inquiry

If you"ve uncovered an concern with this question, please let united state know. V the aid of the ar we can continue to enhance our educational resources.


Do not fill in this field
* her Name:
* concern Description:
DMCA complain

your Infringement notification may be forwarded come the party the made the content easily accessible or to 3rd parties such together ChillingEffects.org.

please follow these steps to paper a notice:

friend must include the following:

Send your complain to our designated certified dealer at:

Charles Cohn Varsity Tutors llc 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105