Solve the reasonable equation:






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









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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


Subtract one top top both sides.

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


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,

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


Then subtract



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


Solve the 2nd equation.



The answer to


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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