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655-705 (Hard)|   Algebra|      
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DeeptiM
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If equation 3x-2y=5 and ax+6y=10 have no common root, a=? Updated on: 04 Jan 2014, 06:05
Originally posted by DeeptiM on 15 Aug 2011, 03:21.
Last edited by Bunuel on 04 Jan 2014, 06:05, edited 1 time in total.
Edited the question and added the OA.
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

60% (01:44) correct 40% (02:13) wrong based on 300 sessions

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Time
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If equation 3x-2y=5 and ax+6y=10 have no common root, a=?

(A) 6
(B) 3
(C) 0
(D) -3
(E) -9
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E
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fluke
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If equation 3x-2y=5 and ax+6y=10 have no common root, a=? 15 Aug 2011, 05:26
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DeeptiM
If equation 3x-2y=5 and ax+6y=10 have no common root, a=?
(A) 6
(B) 3
(C) 0
(D) -3
(E) -9
Show more

If two simultaneous equation are of the form:

\(ax+by=c\)
\(kx+ly=m\)

These equation will have no common root OR in other terms, will be parallel to each other when,
\(\frac{a}{k}=\frac{b}{l} \ne \frac{c}{m}\)---------------1

These equation will have infinite common roots OR have infinite solutions OR in other terms, will coincide/superimpose over each other when,
\(\frac{a}{k}=\frac{b}{l}=\frac{c}{m}\)----------------2

These equation will have just one common root OR in other terms, will intersect each other at one point when,
\(\frac{a}{k} \ne \frac{b}{l}\)-----------------------3

We are concerned about equation 1 here(No common root)

\(\frac{a}{k}=\frac{b}{l} \ne \frac{c}{m}\)

\(3x-2y=5\)
\(ax+6y=10\)

\(\frac{3}{a}=\frac{-2}{6} \ne \frac{5}{10}\)

Or just

\(\frac{3}{a}=\frac{-2}{6}\)

\(a=-9\)

Ans: "E"
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If equation 3x-2y=5 and ax+6y=10 have no common root, a=? 04 Jan 2014, 06:12
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DeeptiM
If equation 3x-2y=5 and ax+6y=10 have no common root, a=?

(A) 6
(B) 3
(C) 0
(D) -3
(E) -9
Show more

\(3x-2y=5\) (\(y=\frac{3x}{2}-\frac{5}{2}\)) and \(ax+6y=10\) (\(y=-\frac{ax}{6}+\frac{10}{6}\)) not to have a common root, lines represented by them must be parallel. Parallel lines have the same slope. Now, the slope of the first line is 3/2, thus the slope of the second line must also be 3/2:

\(\frac{3}{2}=-\frac{a}{6}\) --> \(a=-9\).

Answer: E.
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DeeptiM
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If equation 3x-2y=5 and ax+6y=10 have no common root, a=? 15 Aug 2011, 05:52
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DeeptiM
If equation 3x-2y=5 and ax+6y=10 have no common root, a=?
(A) 6
(B) 3
(C) 0
(D) -3
(E) -9

If two simultaneous equation are of the form:

\(ax+by=c\)
\(kx+ly=m\)

These equation will have no common root OR in other terms, will be parallel to each other when,
\(\frac{a}{k}=\frac{b}{l} \ne \frac{c}{m}\)---------------1

These equation will have infinite common roots OR have infinite solutions OR in other terms, will coincide/superimpose over each other when,
\(\frac{a}{k}=\frac{b}{l}=\frac{c}{m}\)----------------2

These equation will have just one common root OR in other terms, will intersect each other at one point when,
\(\frac{a}{k} \ne \frac{b}{l}\)-----------------------3

We are concerned about equation 1 here(No common root)

\(\frac{a}{k}=\frac{b}{l} \ne \frac{c}{m}\)

\(3x-2y=5\)
\(ax+6y=10\)

\(\frac{3}{a}=\frac{-2}{6} \ne \frac{5}{10}\)

Or just

\(\frac{3}{a}=\frac{-2}{6}\)

\(a=-9\)

Ans: "E"
Show more

Just so I understand clearly..if the question ask for Infinite roots or just one root then the equation must have been as follows:

Infinite Root:

3/a=-2/6=10/5

One Root:

3/a not equal to -2/6 (will the answer then be "a" not a value of?)
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If equation 3x-2y=5 and ax+6y=10 have no common root, a=? 11 Jun 2016, 14:08
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Lines must be parallel.

3x-2y = 5 <-> y =\(\frac{3}{2}\) x - \(\frac{5}{2}\)
ax+6y = 10 <-> y =\(\frac{-a}{6}\) x + \(\frac{5}{3}\)

So, coefficients have to be equal : -a/6 = 3/2 <-> a = -9
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If equation 3x-2y=5 and ax+6y=10 have no common root, a=? 09 Jan 2022, 17:48
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The equations have "no common root" --> means they represent parallel lines.

Any two parallel lines can be put into this form, where n and m are different constants.
ax + by = n
ax + by = m

The two equations are
3x-2y=5
ax+6y=10

Multipy the first by -3, nd the equations become
-9x + 6y = -15
ax + 6y = 10
Since the lines are parallel, a=-9

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If equation 3x-2y=5 and ax+6y=10 have no common root, a=? 24 Jun 2025, 12:37
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