Question
Solve the following simultaneous equations $:\ 2(3u - v) = 5uv,2(u + 3v) = 5uv$
✓
Answer
$2(3 u-v)=5 u v$
$2(u+3 v)=5 u v$
$2(3 u-v)=5 u v$
$\Rightarrow 6 u-2 v=5 u v$
$\Rightarrow \frac{6}{v}-\frac{2}{u}=5 \ldots .(1)$
$2(u+3 v)=5 u v$
$\Rightarrow 2 u+6 v=5 u v$
$\Rightarrow \frac{2}{u}+\frac{6}{v}=5 \ldots . (2) $
Multiplying equation $(1)$ by $3 ,$
we get, $\frac{18}{v}-\frac{6}{u}=15 .....(3) $
Adding $(2)$ and $(3),$
$ \frac{20}{v}=20$
$\Rightarrow v =1$
$\therefore \frac{6}{u}$
$=5-\frac{2}{1}$
$=3$
$\Rightarrow u =\frac{6}{3}$
$=2 $
Thus, the solution set is $(2,1)$.
$2(u+3 v)=5 u v$
$2(3 u-v)=5 u v$
$\Rightarrow 6 u-2 v=5 u v$
$\Rightarrow \frac{6}{v}-\frac{2}{u}=5 \ldots .(1)$
$2(u+3 v)=5 u v$
$\Rightarrow 2 u+6 v=5 u v$
$\Rightarrow \frac{2}{u}+\frac{6}{v}=5 \ldots . (2) $
Multiplying equation $(1)$ by $3 ,$
we get, $\frac{18}{v}-\frac{6}{u}=15 .....(3) $
Adding $(2)$ and $(3),$
$ \frac{20}{v}=20$
$\Rightarrow v =1$
$\therefore \frac{6}{u}$
$=5-\frac{2}{1}$
$=3$
$\Rightarrow u =\frac{6}{3}$
$=2 $
Thus, the solution set is $(2,1)$.
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
Solve :$11(x - 5) + 10(y - 2) + 54 = 0;7(2x - 1) + 9(3y - 1) = 25$
→A briefcase was sold at a profit of $15\%$. If its cost price was $5\%$ less and it was sold for $Rs.35$ less, the gain would have been $20\%$. Find the cost price of the briefcase.
→Find the length of a solid cylinder of diameter $4 \ cm$ when recast into a hollow cylinder of outer diameter $10 \ cm$, thickness $0.25 \ cm$ and length $21 \ cm$? Give your answer correct to two decimal places.
→A $700\ g$ dry fruit pack costs $Rs. 72$. It contains some cashew kernels and the rest as dry grapes. If cashew kernels cost $Rs. 96$ per $kg$ and dry grapes costs $Rs. 112$ per $kg$, what were the quantities of the two dry fruits separately.
→In $\triangle ABC, AD$ is perpendicular to $BC. \sin B = 0.8, BD = 9 \ cm$ and $\tan C = 1.$Find the length of $AB, AD, AC$, and $DC.$
→Express the following decimal as a rational number.$0.763$
→In a rectangle ABCD, AB = 12cm and $\angle$BAC = $30^{\circ}$. Calculate the lengths of side BC and diagonal AC.
→The adjoining diagram shows two cross paths drawn inside a rectangular field 45 m long and 38 m wide, one parallel to length and the other parallel to breadth. The width of each path is 4 m. Find the cost of gravelling the paths at ₹ 5.60 per $m ^2$.
→Two circles touch each other externally. The sum of their areas is $58\pi \ cm^2$ and the distance between their centres us $10\ cm$. Find the radii of the two circles.
→$D, E,$ and $F$ are the mid$-$points of the sides $AB, BC,$ and $CA$ respectively of $\triangle ABC. AE$ meets $DF$ at $O. P$ and $Q$ are the mid$-$points of $OB$ and $OC$ respectively. Prove that $\text{DPQF}$ is a parallelogram.
→