MCQ practice · SSC General Mathematics Board questions · Chapter 12: Simple Simultaneous Equations in Two Variables
The system 5x + 3y = 4, 2x + 7y = 9 - which one is correct?
- i. consistent
- ii. has infinitely many solutions
- iii. mutually independent
Think it through first, then pick an option.
- a i and ii
- b i and iii
- c ii and iii
- d i, ii and iii
Answer and explanation
Correct answer: b i and iii
5/2 ≠ 3/7, so the system is consistent (i) and independent (iii). ii is not true, as the solution is unique.
Why the other options are wrong
- a i and ii: ii is false: 5/2 ≠ 3/7, so there is one solution, not infinitely many. Also the true statement iii is missing here.
- c ii and iii: ii is false: unequal ratios never give infinitely many solutions. Also the true statement i is missing here.
- d i, ii and iii: ii is false: since 5/2 ≠ 3/7 the system has exactly one solution, not infinitely many.
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