Show graphically that each one of the following systems of equations has infinitely many solutions:
$x-2 y=5$
$3 x-6 y=15$
The given equations are
$x-2 y=5$ ...(i)
$3 x-6 y=15$...(ii)
Putting $x=0$ in equation $(i)$, we get:
$\Rightarrow 0-2 y=5$
$\Rightarrow y=-5 / 2$
$x=0, \quad y=-5 / 2$
Putting $y=0$ in equations $(i)$ we get:
$\Rightarrow x-2 \times 0=5$
$\Rightarrow x=5$
$x=5, \quad y=0$
Use the following table to draw the graph.
Draw the graph by plotting the two points $A(0,-5 / 2)$ and $B(5,0)$ from table
Graph of the equation….
$3 x-6 y=15$..(ii)
Putting $x=0$ in equations $(i i)$ we get:
$\Rightarrow 3 x-6 \times 0=15$
$\Rightarrow x=5$
$x=5, \quad y=0$
Use the following table to draw the graph.
Draw the graph by plotting the two points $C(0,-5 / 2)$ and $D(5,0)$ from table.
Thus the graph of the two equations coincide
Consequently, every solution of one equation is a solution of the other.
Hence the equations have infinitely many solutions.
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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,