CA Foundation · Quantitative Aptitude · Equations
For what value of k do the equations 3x + 4y = 10 and 6x + ky = 15 have no solution?
The value is k = 8. For no solution the coefficient ratios of x and y must be equal while the constant ratio differs. Since 3/6 = 4/8 = 1/2 but 10/15 = 2/3, the lines are parallel and never meet.
- Ak = 8Correct
- Bk = 4
- Ck = 6
- Dk = 12
Explanation
No solution requires parallel lines: 3/6 = 4/k ≠ 10/15. From 3/6 = 4/k, k = 8. Then 10/15 = 2/3 ≠ 1/2, so the lines are parallel and distinct. k = 4 would give different slopes and a unique solution.
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