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Presentations Ayuhi

This document provides an overview of linear equations in two variables, defining what an equation is and explaining the characteristics of linear equations. It emphasizes that a linear equation in two variables can be expressed in the form AX + BY + C = 0 and has infinitely many solutions, represented as ordered pairs (X, Y). The document also outlines methods for finding solutions and the graphical representation of these equations as straight lines.

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deep shikha gusain
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12 views9 pages

Presentations Ayuhi

This document provides an overview of linear equations in two variables, defining what an equation is and explaining the characteristics of linear equations. It emphasizes that a linear equation in two variables can be expressed in the form AX + BY + C = 0 and has infinitely many solutions, represented as ordered pairs (X, Y). The document also outlines methods for finding solutions and the graphical representation of these equations as straight lines.

Uploaded by

deep shikha gusain
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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LINEAR EQUATIONS IN TWO

VARIABLES
A JOURNEY INTO THE WORLD OF LINES
CLASS : 9
PRESENTED BY: AYUSHI NEGI
• DEFINITION: AN EQUATION IS A MATHEMATICAL STATEMENT
THAT SHOWS TWO EXPRESSIONS ARE EQUAL. IT CONTAINS
AN EQUALITY SIGN (=).
• * EXAMPLES:

• *5+3=8

• * X + 7 = 10
WHAT IS • * 2Y = 14
AN
EQUATION?
WHAT IS A LINEAR EQUATION?

• DEFINITION: AN EQUATION IN WHICH THE HIGHEST


POWER OF THE VARIABLE (OR VARIABLES) IS 1.
• * WHY “LINEAR”? BECAUSE WHEN PLOTTED ON A
GRAPH, ITS SOLUTIONS FORM A STRAIGHT LINE.
• * EXAMPLES (LINEAR EQUATION IN ONE VARIABLE):
• * X + 5 = 12
• * 3Y = 9
• *Z–2=5
WHAT IS A LINEAR EQUATION IN TWO VARIABLES?

• 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 BOTH ZERO.
• * KEY CHARACTERISTICS:
• * TWO VARIABLES (E.G., X AND Y)
• * HIGHEST POWER OF EACH VARIABLE IS 1.
• * EQUALITY SIGN.
* 2X + 3Y = 5

EXAMPLES * 4X – Y = 7

OF LINEAR * X + Y – 10 = 0

EQUATIONS * Y = 2X – 1 (CAN BE REWRITTEN AS 2X - Y - 1 = 0)

IN TWO
VARIABLES
HOW TO FIND SOLUTIONS?

• ASSUME A VALUE FOR ONE VARIABLE AND SOLVE


FOR THE OTHER.
• * EXAMPLE: FOR 2X + Y = 6
• * IF X = 0, 2(0) + Y = 6 \IMPLIES Y = 6.
SOLUTION: (0, 6)
• * IF Y = 0, 2X + 0 = 6 \IMPLIES X = 3.
SOLUTION: (3, 0)
SOLUTIONS OF A LINEAR EQUATION IN TWO
VARIABLES
• A PAIR OF VALUES (X, Y) THAT SATISFIES THE EQUATION (I.E., MAKES THE EQUATION TRUE
WHEN SUBSTITUTED).
• * IMPORTANT NOTE: A LINEAR EQUATION IN TWO VARIABLES HAS INFINITELY MANY
SOLUTIONS.[WHY? BECAUSE A LINE CONSISTS OF INFINITELY MANY POINTS. EACH POINT ON
THE LINE REPRESENTS A SOLUTION.]
• * A LINEAR EQUATION IN TWO VARIABLES IS OF THE FORM
AX + BY + C = 0.
• * IT HAS INFINITELY MANY SOLUTIONS.

• * EACH SOLUTION IS AN ORDERED PAIR (X, Y).

• * ITS GRAPH IS ALWAYS A STRAIGHT LINE.


• * WE CAN FIND SOLUTIONS BY SUBSTITUTING VALUES AND
CAN GRAPH THEM TO VISUALIZE THE RELATIONSHIP.

SUMMARY
“THANK YOU FOR
YOUR
ATTENTION!

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