Solve the following system of linear equations graphically :
3x + y − 11 = 0, x − y − 1 = 0.
Shade the region bounded by these lines and y-axis. Also, find the area of the region bounded by the these lines and y-axis.
The given equations are
$3 x+y-11=0$$\ldots \ldots($ i $)$
$x-y-1=0$$\ldots \ldots($ ii $)$
Putting $x=0$ in equation $(i)$, we get:
$\Rightarrow 3 \times 0+y=11$
$\Rightarrow y=11$
$x=0, \quad y=11$
Putting $y=0$ in equation $(i,$, we get:
$\Rightarrow 3 x+0=11$
$\Rightarrow x=11 / 3$
$x=11 / 3, \quad y=0$
Use the following table to draw the graph.
Draw the graph by plotting the two points from table.
$x-y=1$ ..(ii)
Putting $x=0$ in equation $(i i)$ we get:
$\Rightarrow 0-y=1$
$\Rightarrow y=-1$
$x=0, \quad y=-1$
Putting $y=0$ in equation $(i i)$, we get:
$\Rightarrow x-0=1$
$\Rightarrow x=1$
$x=1, \quad y=0$
Use the following table to draw the graph.
Draw the graph by plotting the two points from table.
The two lines intersect at $P(3,2)$.
Hence $x=3$, $y=2$ is the solution of the given equations
The area enclosed by the lines represented by the given equations and the y−axis is shaded region in the figure
Now, Required area = Area of shaded region
$\Rightarrow$ Required area $=$ Area of PAC
$\Rightarrow$ Required area $=1 / 2($ base $\times$ height $)$
$\Rightarrow$ Required area $=1 / 2(A C \times P M)$
$\Rightarrow$ Required area $=1 / 2(12 \times 3)$ sq.units
Hence the required area is 18 sq. unit
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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,