In each of the following cases, find a and b.
(i) (2a + b, a – b) = (8, 3)
(ii) (a/4 , a – 2b) = (0, 6 + b)
(i)
According to the question,
(2a + b, a – b) = (8, 3)
Given the ordered pairs are equal, so corresponding elements will be equal.
Hence,
2a + b = 8 and a–b = 3
Now a–b = 3
⇒a = 3 + b
Substituting the value of a in the equation 2a + b = 8,
We get,
2(3 + b) + b = 8
⇒ 6 + 2b + b = 8
⇒ 3b = 8–6 = 2
⇒ b = 2/3
Substituting the value of b in equation (a–b = 3),
We get,
⇒ a – 2/3 = 3
⇒ a = 3 + 2/3
⇒ a = (9 + 2)/3
⇒ a = 11/3
Hence the value of a = 11/3 and b = 2/3 respectively.
(ii)
According to the question,
$\left(\frac{a}{4}, a-2 b\right)=(0,6+b)$
Given the ordered pairs are equal, so corresponding elements will be equal.
a/4 = 0 and a – 2b = 6 + b
Now a/4 = 0
⇒a = 0
Substituting the value of a in the equation (a–2b = 6 + b),
We get,
0 – 2b = 6 + b
⇒ – 2b – b = 6
⇒ – 3b = 6
⇒ b = – 6/3
⇒ b = – 2
Hence, the value of a = 0 and b = – 2 respectively
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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,