This is a power point presentation on linear equations in two variables for class 10th. I have spent 3 hours on making this and all the equations you will see are written by me.
AN EQUATION WHICH CAN BE WRITTEN IN THE FORM OF ax+by+c=0 WHERE a,b and c ARE REAL NUMBERS.
YOU WILL GET TO KNOW HOW TO REPRESENT THE EQUATIONS IN A GRAPH.
AN EQUATION WHICH CAN BE WRITTEN IN THE FORM OF ax+by+c=0 WHERE a,b and c ARE REAL NUMBERS.
YOU WILL GET TO KNOW HOW TO REPRESENT THE EQUATIONS IN A GRAPH.
Pair Of Linear Equations In Two VariablesDeo Baran
PowerPoint Presentation of Learning Outcomes, Experiential content, Explanation Content, Hot Spot, Curiosity Questions, Mind Map, Question Bank of
Pair Of Linear Equations In Two Variables Class X
Order of presentation
Anushka - Opening
Nikunj -Intro
Shubham - Graphical
Amel - Sunstitution
Siddhartha- Elimination
Karthik - Cross multiplication
Anushka - Equations reducible...& wrap-up
In case of any confusion..inform me by facebook, phone or in school
Power Point Presentation on a PAIR OF LINEAR EQUATION IN TWO VARIABLES, MATHS project...
Friends if you found this helpful please click the like button. and share it :) thanks for watching
Pair Of Linear Equations In Two VariablesDeo Baran
PowerPoint Presentation of Learning Outcomes, Experiential content, Explanation Content, Hot Spot, Curiosity Questions, Mind Map, Question Bank of
Pair Of Linear Equations In Two Variables Class X
Order of presentation
Anushka - Opening
Nikunj -Intro
Shubham - Graphical
Amel - Sunstitution
Siddhartha- Elimination
Karthik - Cross multiplication
Anushka - Equations reducible...& wrap-up
In case of any confusion..inform me by facebook, phone or in school
Power Point Presentation on a PAIR OF LINEAR EQUATION IN TWO VARIABLES, MATHS project...
Friends if you found this helpful please click the like button. and share it :) thanks for watching
How to Create Map Views in the Odoo 17 ERPCeline George
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
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Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
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An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
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Sectors of the Indian Economy - Class 10 Study Notes pdf
Linear equations in two variables- By- Pragyan
1. Made by – Group 4
Group name- G. Cantor
Group leader- Pragyan
Members- Aditya
Prashant
Bhisham
Anshul
Shubham
2. Linear Equations
A linear equation in two variable x and y is an equation that
can be written in the form ax + by + c = 0, where a ,b and c
are real numbers and a and b are not equal to 0.
Example of a linear equation in two variables is 2x+4y=60
3. Solution of an Equation in Two Variables
Example:
Given the equation 2x + 3y = 18, determine if the
ordered pair (3, 4) is a solution to the equation.
Solution:
We substitute 3 in for x and 4 in for y.
2(3) + 3 (4) ? 18
6 + 12 ? 18
18 = 18 True.
Therefore, the ordered pair (3, 4) is a solution to the
equation 2x + 3y = 18.
4. The Rectangular Coordinate
System
In the rectangular coordinate system, the horizontal number line
is the x-axis.
The vertical number line is the y-axis.
The point of intersection of these axes is their zero points, called
the origin. The axes divide the plane into 4 quarters, called
quadrants.
5. CARTESIAN PLANE
Quadrant II
( - ,+)
Quadrant I
(+,+)
Quadrant IV
(+, - )
Quadrant III
( - , - )
y-axis
x- axis
6. Plotting Points on a Graph Paper
EXAMPLE Plot the points (3,2) and (-2,-4).
SOLUTION
7. Solution for a linear equation in two variables
Let ax + by +c = O , where a ,b , c are real numbers
such that a and b ≠ O. Then, any pair of values of x
and y which satisfies the equation ax + by +c = O, is
called a solution of it.
8.
9. Graphical
Method Example
Solve the following system of linear equations:
Since we are seeking out the point of intersection, we may graph the equations:
We see here that the lines intersect each other at the point x = 2, y = 8. This is
our solution and we may refer to it as a graphic solution to the task.
10. Substitution
method
The method of solving "by substitution" works by
solving one of the equations (you choose which one)
for one of the variables (you choose which one), and
then plugging this back into the other equation,
"substituting" for the chosen variable and solving for
the other. Then you back-solve for the first variable.
11. For example if the equations are
푥 − 2푦 = 10…… (i) and 2푥 + 푦 = 30………. (ii)
From (i) we get 푥 = 10 + 2푦
So now we put the value of x in equation (ii)….
2 10 + 2푦 + 푦 = 30
Or, 20 + 5푦 = 30 Or, 푦 =
10
5
Or, 푦 = 2
Putting the value of y in equation (i)
i.e. 푥 − 2 2 = 10
or, 푥 = 10 + 4 표푟, 푥 = 14
12. Elimination
In the eliMmineattiohn moedthod we eliminate
either of the variables to solve the
equation.
We first make the coefficients of the
variable equal in both the equations by
multiplying the whole equation by an
integer except zero. Then we eliminate the
variable and solve the equation for the
value of another variable.
13. For example if the equations are
푥 − 2푦 = 10…… (i) and 2푥 + 푦 = 30………. (ii)
First we make the coefficient of x in equation (i) equal to that of
equation (ii). So, we multiply the whole equation by 2 we get,
2푥 − 4푦 = 20 … … … (푖푖푖)
Now we can either subtract (ii) by (iii) or vice versa.
So, subtracting (iii) by (ii) we get,
2푥 + 푦 − 2푥 − 4푦 = 30 − 20
푂푟, 2푥 + 푦 − 2푥 + 4푦 = 10
푂푟, 5푦 = 10 푖. 푒. 푦 =
10
5
푖. 푒. 푦 = 2
Now we put the value of y in equation (iii) we get,
2푥 − 4 2 = 20
푖. 푒. 2푥 = 20 + 8
푖. 푒. 2푥 = 28 표푟, 푥 =
28
2
표푟, 푥 = 14
14. Cross
multiplication
method
Let’s consider the general form of a pair of linear equations a1x + b1y + c1 = 0 , and a2x +
b2y + c2 = 0.
When a1 divided by a2 is not equal to b1 divided by b2, the pair of linear equations will
have a unique solution.
To solve this pair of equations for x and y using cross-multiplication, we’ll arrange the
variables x and y and their coefficients a1, a2, b1 and b2, and the constants c1 and c2 as
shown
15. For example if the equations are
푥 − 2푦 = 10…… (i) and 2푥 + 푦 = 30………. (ii)
First we write it in this form as
푥 − 2푦 − 10 = 0 푎푛푑 2푥 + 푦 − 30 = 0
According to the theory
푥
−2 − 10
1 − 30
=
푦
−10 1
−30 2
=
1
1 − 2
2 1
Cross multiplying we get,
푥
−10 − 60
=
푦
−30 − −20
=
1
−4 − 1
푖푒.
푥
−70
=
푦
−10
=
1
−5
푥
−70
=
1
−5
푖푒. −5푥 = −70 푖푒. 푥 = −
70
−5
표푟, 푥 = 14
푦
−10
=
1
−5
푖푒. −5푦 = −10 푖푒. 푦 = −
10
−5
푖푒. 푦 = 2
16. Equations reducible to a
pair of linear equations in
two variables
Q. Solve the pair of equations
2
푥
+
3
푦
= 13
5
푥
−
4
푦
= −2
Sol. Let us write the equations as
2
1
푥
+ 3
1
푦
= 13
5
1
푥
− 4
1
푦
= −2
17. We let
1
푥
= 푝 푎푛푑
1
푦
= 푞
Thus the equation becomes,
2푝 + 3푞 = 13 푎푛푑 5푝 − 4푞 = −2
Now you can use any method to get p=2 and q=3
Substituting the values of p and q to get,
1
푥
= 2 푖푒. , 푥 =
1
2
푎푛푑
1
푦
= 3 푖푒. , 푦 =
1
3