Solve the following systems of equations:
$\frac{10}{x+y}+\frac{2}{x-y}=4$
$\frac{15}{x+y}-\frac{9}{x-y}=-2$
The given equations are:
$\frac{10}{x+y}+\frac{2}{x-y}=4$
$\frac{15}{x+y}-\frac{9}{x-y}=-2$
Let $\frac{1}{x+y}=u$ and $\frac{1}{x-y}=v$ then equations are
$10 u+2 v=4 \ldots(i)$
$15 u-9 v=-2 \ldots(i i)$
Multiply equation $(i)$ by 9 and equation $(i i)$ by 2 and add both equations, we get
Put the value of $u$ in equation $(i)$, we get
$10 \times \frac{32}{120}+2 v=4$
$\Rightarrow 2 v=\frac{16}{12}$
$\Rightarrow v=\frac{8}{12}$
Then
$\frac{1}{x+y}=\frac{32}{120}$
$\Rightarrow x+y=\frac{120}{32} \quad \ldots(i i i)$
$\frac{1}{x-y}=\frac{8}{12}$
$\Rightarrow x-y=\frac{12}{8} \ldots(i v)$
Add both equations, we get
$x+y=\frac{120}{32}$
Put the value of $x$ in equation $(i i i)$ we get
$1 \times \frac{21}{8}+y=\frac{120}{32}$
$\Rightarrow y=\frac{9}{8}$
Hence the value of $x=\frac{21}{8}$ and $y=\frac{9}{8}$.
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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,