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The cost of 2 kg apples and 1 kg of grapes on a day was found to be ₹ 320. The cost of 4 kg apples and 2 kg grapes was found to be ₹ 600. If cost of 1 kg of apples and 1 kg of grapes is ₹ x and ₹ y respectively, represent the given situation algebraically as a system of equations and check whether the system so obtained is consistent or not.
Solve for x and y : √2 x + √3 y = 5 and √3 x − √8 y = −√6
Assertion (A) : The pair of linear equations px + 3y + 59 = 0 and 2x + 6y + 118 = 0 will have infinitely many solutions if p = 1. Reason (R) : If the pair of linear equations px + 3y + 19 = 0 and 2x + 6y + 157 = 0 has a unique solution, then p ≠ 1.
Which of the following is a condition for unique solution of a pair of linear equations?
Assertion (A): The pair 2x + 3y = 8 and 4x + 6y = 10 has a unique solution. Reason (R): Lines with different slopes intersect at one point.
Find the value of k so that the pair x + 2y = 5 and 3x + ky + 15 = 0 has a unique solution.
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