Question

32/x+3-33/y+2=97 33/x+3-32/y+2=98

Answer 1

Step-by-step explanation:

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Answer 2

$Given \: system \:of \: questions : \\\frac{32}{x+3} - \frac{33}{y+2} = 97 \: --(1)$

$and \: \frac{33}{x+3} - \frac{32}{y+2} = 98 \: --(2)$

$Let \: a = \frac{1}{x+3}\: and b = \frac{1}{y+2}$

$Rewrite \:the \: equations , we \:get$

$32a - 33b = 97 \: --(3) \: and \\ 33a - 32b = 98 \: --(4)$

/* Multiplying equation (3) with 33 and equation (4) with 32 , we get*/

$1056a - 1089b = 3201 \: --(5) \\and \: 1056a - 1024b = 3136 \: --(6)$

/ * Subtract equation (5) from equation (6), we get*/

$\implies 65b = -65$

$\implies b = -1$

$Put \: b = -1 \: in \: equation \:(4) ,\\we \:get$

$33a - 32 \times (-1) = 98$

$\implies 33a + 32 = 98$

$\implies 33a = 98- 32$

$\implies 33a = 66$

$\implies a = \frac{66}{33}$

$\implies a = 2$

$a = \frac{1}{x+3} = 2$

$\implies x + 3 = \frac{1}{2}$

$\implies x = \frac{1}{2} - 3$

$\implies x = \frac{1-6}{2}$

$\implies x = \frac{-5}{2}$

$and \: b = \frac{1}{y+2} = -1$

$\implies y+2 = -1$

$\implies y = -1 - 2$

$\implies y = -3$

Therefore.,

$\green { x = \frac{-5}{2} }$

$\green { y = -3}$

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