Question 24316: 9x+6y=14
3x+2y=11
Solve for x and y
I know that you have to use substitution but i keep getting answers like,
9x+66-9x=14 so it is going to turn out with your x's turning into a zero and you come out with 0=52 and that is obviousley not true...PLEASE HELP ASAP I have been working on this for at least an hour
i looked for examples similiar to this problem but i could'nt find any
Found 4 solutions by venugopalramana, MathTherapy, timofer, greenestamps:
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! SEE MY COMMENTS BELOW.
9x+6y=14
3x+2y=11
Solve for x and y
I know that you have to use substitution but i keep getting answers like,
9x+66-9x=14 so it is going to turn out with your x's turning into a zero and you come out with 0=52 and that is obviousley not true.
THERE IS NOTHING WRONG WITH YOU !POOR BOY !YOU HAVE BEEN TRYING TOO HARD TO ACHIEVE THE IMPOSSIBLE.SEE A PROBLEM GIVEN BELOW TO UNDERSTAND THE PHENOMENA.
SO BELIEVE IN YOUR SELF ,YOUR WORK AND SAY FIRMLY THERE IS NO SET OF VALUES OF X AND Y WHICH SATISFY THE 2 GIVEN EQUATIONS.SEE MY COMMENTS AT THE END OF THE EXAMPLE BELOW FOR A SPECIFIC POINT ON YOUR PROBLEM..
..PLEASE HELP ASAP I have been working on this for at least an hour
i looked for examples similiar to this problem but i could'nt find any
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In the given system of equations is consistent and dependent, consistent and independent or inconsistent.
3x-y=7
6x-2x=9
what does these terms mean?
1 solutions
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Answer 12951 by venugopalramana(684) on 2006-01-13 01:20:47 (Show Source):
IS the given system of equations consistent
MEANS WHETHER THERE IS ANY SET OF VALUES FOR X AND Y WHICH SATISFIES BOTH THE GIVEN EQUATIONS.
and dependent,MEANS WHETHER ONE EQUATION CAN BE GOT FROM THE OTHER BY SUITABLE AND PERMISSIBLE TRANSFORMATION
consistent and independent,MEANS THAT ONE EQUATION CANNOT BE OBTAINED FROM THE OTHER EQUATION BY BY ANY SUITABLE AND PERMISSIBLE TRANSFORMATION .
or inconsistent.MEANS THERE ARE NO SET OF VALUES FOR X AND Y WHICH SATISFY BOTH THE EQUATIONS.
3x-y=7.....I.......
6x-2x=9...I THINK IT SHOULD BE 6X-2Y=9........II
what does these terms mean?NOW I THINK YOU KNOW WHAT THE TERMS MEAN.THERE ARE TESTS FOR FINDING THESE SITUATIONS.WE SHALL RESTRICT THE ANALYSIS TO YOUR PROBLEM AFTER THE CORRECTION MENTIONED ABOVE.
WE FIND THAT ON L.H.S OF THE 2 EQNS.WE HAVE 3X-Y AND 6X-2Y WHICH ARE DIRECT MULTIPLES BY 2 .THAT IS WE GET LHS OF EQN.2 BY MULTIPLYING THE EQN 1 WITH 2
WE GET EQN.I *2 ....6X-2Y=14
WHERE AS EQN.II SAYS 6X-2Y=9..SO IF WE TRY TO SATISFY EQN.I ,EQN II WILL NOT BE SATISFIED AND IF WE TRY TO SATISFY EQN II ,EQN.I WILL NOT BE SATISFIED.SO THERE ARE NO VALUES OF X AND Y WHICH SATISFY BOTH EQUATIONS.SO WE SAY THE GIVEN EQNS. ARE INCONSISTENT.
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IN YOUR PROBLEM THE LHS OF FIRST EQN IS OBTAINED BY MULTIPLYING WITH 3 THE LHS OF SECOND EQN
SO 9X+6Y=42 AND NOT 11 AS GIVEN HENCE THEY ARE INCONSISTENT AND THERE IS NO SOLUTION.IF YOU WANT TO LEARN MORE ON THIS COME BACK .
Answer by MathTherapy(10803)  (Show Source):
You can put this solution on YOUR website!
9x+6y=14
3x+2y=11
Solve for x and y
I know that you have to use substitution but i keep getting answers like, 9x+66-9x=14 so it is going
to turn out with your x's turning into a zero and you come out with 0=52 and that is obviousley not
true...PLEASE HELP ASAP I have been working on this for at least an hour
i looked for examples similiar to this problem but i could'nt find any
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The other person seems to be saying a lot, but in this author's opinion, it's TOO MUCH, and
can easily confuse someone, as opposed to helping him/her to understand this problem and
then provide a reasonable and logical answer.
9x + 6y = 14 ---- eq (i)
3x + 2y = 11 ---- eq (ii)
- 9x - 6y = - 33 ----- Multiplying eq (ii) by - 3 --- eq (iii)
0 = - 19 ----- Adding eqs (i) & (iii)
0 = - 19 is a FALSE statement, and shows that:
1) there are NO SOLUTIONS to this system
2) the system is INCONSISTENT
3) the 2 equations are parallel, have the same slope, and as such, will NEVER INTERSECT
Answer by timofer(155)  (Show Source):
Answer by greenestamps(13326)  (Show Source):
You can put this solution on YOUR website!
You say you are ending up with an equation that says something like "0=52".
You are probably doing the algebra correctly; now you just need to learn what that result means.
As you say, "0=52" is not true; that equation has no solutions. Assuming you did the algebra correctly, that means the original pair of equations has no solution.
When you are first learning algebra, it is important that you recognize this kind of result and understand what it means.
An experienced student can look at this pair of equations and see that the "9x+6y" in the first equation is just 3 times the "3x+2y" in the second equation. If you see that, then you can multiply the second equation by 3, making the pair of equations
9x+6y=14
9x+6y=-33
The expressions on the left are identical, so the expressions on the right should be identical. Since they are not, the system of equations has no solution.
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