Question

7/x+8/y=2 and 2/x+13/y=22
​

Answer 1

x = - ¹/₂ , y = ¹/₂

Given

$\rm \dfrac{7}{x}+\dfrac{8}{y}=2...(1)\\\\\rm \dfrac{2}{x}+\dfrac{13}{y}=22...(2)$

To Find

x and y values

Solution

Multiply eq. (1) by 2 ,

$\to \rm 2\left(\dfrac{7}{x}+\dfrac{8}{y}\right)=2(2)\\\\\to \rm \dfrac{14}{x}+\dfrac{16}{y}=4...(3)$

Multiply eq. (2) by 7 ,

$\to \rm 7\left(\dfrac{2}{x}+\dfrac{13}{y}\right)=7(22)\\\\\to \rm \dfrac{14}{x}+\dfrac{91}{y}=154...(4)$

Solve (4) - (3) ,

$\to \rm \left(\dfrac{14}{x}+\dfrac{91}{y}\right)-\left(\dfrac{14}{x}+\dfrac{16}{y}\right)=154-4\\\\\to \rm \dfrac{75}{y}=150\\\\\to \bf \pink{y=\dfrac{1}{2}\ \; \bigstar}$

Sub. y value in (1) ,

$\to \rm \dfrac{7}{x}+\dfrac{8}{(\frac{1}{2})}=2\\\\\to \rm \dfrac{7}{x}+2(8)=2\\\\\to \rm \dfrac{7}{x}=2-16\\\\\to \rm \dfrac{7}{x}=-14\\\\\to \rm x=-\dfrac{7}{14}\\\\\to \bf \green{x=-\dfrac{1}{2}\ \; \bigstar}$

Answer 2

Answer:

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