SOLUTION: In the process of solving an equation, if the variable is eliminated the answer is always, sometimes or never "no solution"?

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Question 1110041: In the process of solving an equation, if the variable is eliminated the answer is always, sometimes or never "no solution"?
Found 3 solutions by josgarithmetic, ikleyn, TeachMath:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!
Is the final statement true or is it false?

Have you something that results in maybe -1=5? FALSE STATEMENT, and equation from which it came has no solution.

Have you something resulting in something like 12=12, or -0.5=-0.5 ?
This would seem to indicate always true, the original equation.

Do you have example equations to start with?

Answer by ikleyn(52804)   (Show Source):
You can put this solution on YOUR website!
.
The answer to your question is "SOMETIMES".

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To learn more, see the lessons
    - Solution of the linear system of two equations in two unknowns by the Substitution method
    - Solution of the linear system of two equations in two unknowns by the Elimination method
    - Solution of the linear system of two equations in two unknowns using determinant
    - Geometric interpretation of the linear system of two equations in two unknowns (*)
in this site, especially, the lesson marked (*) in the list.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

Answer by TeachMath(96)   (Show Source):
You can put this solution on YOUR website!
sometimes