Question
Solve the following simultaneous equation.
$\frac{2}{x}-\frac{3}{y}=15 ; \frac{8}{x}+\frac{5}{y}=77$
$\frac{2}{x}-\frac{3}{y}=15 ; \frac{8}{x}+\frac{5}{y}=77$
✓
Answer
$\frac{2}{x}-\frac{3}{y}=15$
$\frac{8}{x}+\frac{5}{y}=77$
Let $\frac{1}{x}=m$ and $\frac{1}{y}=n$
$2 m-3 n =15 \ldots (I)$
$8 m+5 n =77 \ldots (II)$
Multiply Eq. $1$ by $4$
$8 m-12 n =60 \ldots (III)$
Equating Eq. $II$ and $III$. Change the signs of Eq. $III$
$8 m+5 n=77$
$\frac{-8 m+12 n=-60}{17 n=17}$
$n=\frac{17}{17}$
$n=1$
Substituting $n =1$ in Eq. $II$
$8 m+5 \times 1=77$
$8 m+5=77$
$8 m=77-5$
$8 m=72$
$m=\frac{72}{8}$
$m=9$
$\therefore m =\frac{1}{ x } \Rightarrow \frac{1}{ x }=9 \Rightarrow x =\frac{1}{9}$
$\therefore n =\frac{1}{ y } \Rightarrow \frac{1}{ y }=1 \Rightarrow y =1$
Hence $( x , y )=\left(\frac{1}{9}, 1\right)$
$\frac{8}{x}+\frac{5}{y}=77$
Let $\frac{1}{x}=m$ and $\frac{1}{y}=n$
$2 m-3 n =15 \ldots (I)$
$8 m+5 n =77 \ldots (II)$
Multiply Eq. $1$ by $4$
$8 m-12 n =60 \ldots (III)$
Equating Eq. $II$ and $III$. Change the signs of Eq. $III$
$8 m+5 n=77$
$\frac{-8 m+12 n=-60}{17 n=17}$
$n=\frac{17}{17}$
$n=1$
Substituting $n =1$ in Eq. $II$
$8 m+5 \times 1=77$
$8 m+5=77$
$8 m=77-5$
$8 m=72$
$m=\frac{72}{8}$
$m=9$
$\therefore m =\frac{1}{ x } \Rightarrow \frac{1}{ x }=9 \Rightarrow x =\frac{1}{9}$
$\therefore n =\frac{1}{ y } \Rightarrow \frac{1}{ y }=1 \Rightarrow y =1$
Hence $( x , y )=\left(\frac{1}{9}, 1\right)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Write the expression of the common difference of an A.P. whose first term is a and $n^{th}$ term is b.
→The difference of squares of two numbers is $180.$ The square of the smaller number is $8$ times the larger number. Find two numbers.
→D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}$ such that DE || BC: If $\frac{\text{AD}}{\text{AB}}=\frac{8}{15}$ and EC = 3.5cm, find AE.
→If 1 is added to the numerator of a certain fraction its value becomes $\frac{1}{2}$ and if 1 is added to its denometer $\frac{1}{3}$. Find the original fraction.
→Two poles of heights $6m$ and $11m$ stand on a plane ground. If the distance between their feet is $12m$, find the distance between their tops.
→If $\sqrt{3}\tan\theta=3\sin\theta,$ find the value of $\sin^2\theta-\cos^2\theta$.
→Find the value of $k$ for which given quadratic equation are real and equal roots.
$4 x^2-3 k x+1=0$
→$4 x^2-3 k x+1=0$
Prove the following trigonometric identities.
$\frac{\tan\text{A}}{1+\sec\text{A}}-\frac{\tan\text{A}}{1-\sec\text{A}}=2\text{cosec A}$
→$\frac{\tan\text{A}}{1+\sec\text{A}}-\frac{\tan\text{A}}{1-\sec\text{A}}=2\text{cosec A}$
If the HCF of 657 and 963 is expressible in the form 657x + 963x - 15, find x.
Figure shows a sector of a circle of radius r cm containing an angle $\theta.$ The area of the sector is A cm$^2$ and perimeter of the sector is 50cm. Prove that.$\theta=\frac{360}{\pi}\Big(\frac{25}{\text{r}}-1\Big)$
→