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. 


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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.


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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


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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:

*


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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.


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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. 


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