there are two number. four times of the first one exceeds by 2 from 7

1.	there are two number. four times of the first one exceeds by 2 from 7 times of the second one . Sum of two times of the first and three times of the second is 92 . Find the number
Answer» ONG>Step-by-step explanation: Correct Question:- Find two numbers such that the sum of twice the first and THRICE the second is 92, and four times the first EXCEEDS seven times the second by 2. $\bf\underline{\underline{\red{Given:-}}}$ Two numbers are such that sum of twice the first and thrice the second is 92. Four times the first exceeds seven times the second by 2. $\bf\underline{\underline{\blue{To\:Find:-}}}$ The two numbers. $\bf\underline{\underline{\green{Solution:-}}}$ $\sf Let \: the \: first \: number \: be \: x$ $\sf And, \: second \: number \: be \: y$ $\bf {\underline{\pink{Case\: 1:-}}}$ Sum of twice the first and thrice the second is 92. $\sf 2( First \: number) + 3(Second\: number) = 92$ $\sf \implies 2x + 3y = 92.....(i)$ $\bf{\underline{\orange{Case\: 2:-}}}$ Four times the first exceeds seven times the second by 2. $\sf 4(First\: number) - 7(Second\: number) = 2$ $\sf \implies 4x - 7y = 2.....(ii)$ $\sf Multiply \: the \: equation\: (i) \: with\: 2$ $\sf \implies 2(2x + 3y = 92)$ $\sf \implies 4x + 6y = 184.....(iii)$ $\sf\underline{ Subtracting \: equation\: (ii) \: from \: (iii)}$ $\sf \implies 4x + 6y - (4x - 7y) = 184 - 2$ $\sf \implies 4x + 6y - 4x + 7y = 182$ $\sf \implies 13y = 182$ $\sf \implies y = \dfrac{182}{13} = 14$ $\sf Substituting\: y = 14\: in \: equation \: (i)$ $\sf\implies 2x + 3y = 92$ $\sf \implies 2x + 3(14) = 92$ $\sf \implies 2x + 42 = 92$ $\sf \implies 2x = 92 - 42$ $\sf\implies 2x = 50$ $\sf \implies x = 25$ $\sf \underline{We\: have:-}$ $\sf \dashrightarrow First \: number = x = 25$ $\sf \dashrightarrow Second \: number = y = 14$ $\underline{\boxed{\purple{\rm \therefore The\: two\: numbers \: are \: 25 \: and \: 14}}}$