CAT Sample Questions - Question 4 the day : August 05, 2004
The question for the day is from the topic linear equations in Algebra.
For what values of ‘k’ will the pair of equations 3x + 4y = 12 and kx + 12y = 30 not have a unique solution?
| (1) |
12
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(2) |
9
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| (3) |
3
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(4) |
7.5
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Correct choice - (2) Correct Answer -(9)
Explanatory Answer
A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. That is, if they are not parallel lines.
ax + by + c = 0 and dx + ey + g = 0 will not be parallel lines if 
In the above question, we need  or k should not be equal 9 for the pair of equations to have a unique solution.
In other words, when k = 9, the system of equation will not have any solution as the two lines represented by the equations will be parallel lines.
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