Question

When 5 times the larger of the two numbers is divided by the smaller , the quotient and the remainder is 2 and 9 respectively . Form a linear equation in two variables

Answer 1

Let the larger number be x and smaller number be y
Five times larger number = 5x
When 5x is divided by y the quotient is 2 and remainder is 9.
By division rule, we have
Dividend = (divisor) × (quotient) + Remainder
5x = y(2) + 9
⇒ 5x – 2y – 9 = 0
Put x = 3 and y = 3 in LHS
5x – 2y – 9 = 5(3) – 2(3) – 9
= 15 – 15 = 0
= RHS
Hence x = 3 and y = 3 is one of the solution of the linear equation.