Solve each of the following systems of equations by the method of cross-multiplication :
$\frac{5}{x+y}-\frac{2}{x-y}=-1$
$\frac{15}{x+y}+\frac{7}{x-y} 10$
where $x \neq 0$ and $y \neq 0$
GIVEN:
$\frac{5}{x+y}-\frac{2}{x-y}=-1$
$\frac{15}{x+y}+\frac{7}{x-y}=10$
To find: The solution of the systems of equation by the method of cross-multiplication:
Here we have the pair of simultaneous equation
Rewriting the equation again
$\frac{5}{x+y}-\frac{2}{x-y}+1=0$
$\frac{15}{x+y}+\frac{7}{x-y}-10=0$
Taking $u=\frac{1}{x+y}$ and $v=\frac{1}{x-y}$
$5 u-2 v+1=0$...(1)
$15 u+7 v-10=0$...$.(2)$
By cross multiplication method we get
$\frac{u}{(20)-(7)}=\frac{-v}{(-50)-(15)}=\frac{1}{(35)-(-30)}$
$\Rightarrow \frac{u}{13}=\frac{-v}{-65}=\frac{1}{65}$
$\Rightarrow \frac{u}{13}=\frac{v}{65}=\frac{1}{65}$
$\Rightarrow \frac{u}{13}=\frac{1}{65}$
$\Rightarrow u=\frac{1}{5}$
And
$\frac{v}{65}=\frac{1}{65}$
$v=1$
We know that
$u=\frac{1}{x+y}$ and $v=\frac{1}{x-y}$
$\Rightarrow \frac{1}{5}=\frac{1}{x+y}$
$\Rightarrow x+y=5 \quad \ldots \ldots . .(3)$
and
$1=\frac{1}{x-y}$
$\Rightarrow x-y=1$ $...(4)$
Adding equation (3) and (4)
$2 x=6$
$x=3$
Substituting value of x in equation (3) we get
$\begin{aligned} y &=5-3 \\ &=2 \end{aligned}$
$=2$
Hence we get the value of $x=3$ and $y=2$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,