CA Foundation · Quantitative Aptitude · Equations
For what value of k will the system 2x + 3y = 7 and 4x + ky = 14 have infinitely many solutions?
The value of k is 6. For infinitely many solutions, the second equation must be a multiple of the first. Since 4x and 14 are exactly double 2x and 7, the y-coefficient must also double from 3 to 6.
- A3
- B12
- C6Correct
- D7
Explanation
Infinitely many solutions need the coefficient ratios to be equal: 2/4 = 3/k = 7/14. Since 2/4 = 1/2 and 7/14 = 1/2, we need 3/k = 1/2, so k = 6. Choosing k = 3 would give 4x + 3y = 14, which is not a multiple of the first equation.
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