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**LINEAR EQUATIONS Mrs. Chanderkanta -9x - 4x = -36 9x - 4x = -36**

3x-4y =7 3x –7y =21 Mrs. Anju Mehta 5x –8y =-40 -6x +7y = 42 2x+ 3y =6 3x –7y =21

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Target group Class ninth and tenth

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**LEARNING OBJECTIVES Define the linear equation in two variable.**

Solution of linear equation. Converts a linear equation of two variable in graphical form . Solve simultaneous linear equation by graphical method. Learn computer skills. Learn about MS Office. Develop a habit of research. Learn to insert the pictures and relevant text in their presentation . Learn editing skill.

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**WHEN we talk to each other, we use sentences.**

What do we say? Either we talk or we give some statements These statements may be RIGHT or WRONG For example we make the statement- ”sunrises in the east and sets in the west”

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**WHEN we talk to each other, we use sentences.**

What do we say? Either we talk or we give some statements These statements may be RIGHT or WRONG For example we make the statement- ”sunrises in east and sets in west” This is a TRUE statement It is not necessary that all the statements are true. Some are true and some are false. In mathematics we call those statements as OPEN STATEMENTS

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If an open statement becomes TRUE for some value then it is called EQUALITY and it is represented by the sign “ = “ An EQUALITY has two sides L.H.S. and R.H.S. where, L.H.S. = R.H.S.

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**In mathematics, we often use OPEN STATEMENTS**

For example the statement , “ any number added to 5 will give 8” is an open statement If we add any number to 5, we may or may not get 8 5 + 1= 8 FALSE STATEMENT FALSE STATEMENT 5 + 2 = 8 5 + 3 = 8 TRUE STATEMENT The number 3 makes both the sides equal. Hence the statement becomes TRUE.

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**How much weight should be added to equalize the balance?**

2 kg 5 kg How much weight should be added to equalize the balance? + 2 kg = 5 kg

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+ 2kg = 5kg The above statement becomes x+ 2= 5 This statement is called an EQUATION This equation will be true depending on the value of the variable ‘x’

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So we can say, ax+b = 0 is an equation in one variable x Where a,b are constants & a =

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**Let us take an example from daily life.**

Cost of two rubbers and three pencils is six rupees In mathematical form, it can be written as 2x + 3y = 6, where x is the cost of one rubber and y of one pencil x 3 y 2 (3, 0) (0,2) Ordered pairs

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**Let us plot the ordered pairs:**

(3,0) Show me (0,2) Show me Y- axis 3 (0,2) 2 * 2x + 3y =6 1 (3,0) * -3 -2 -1 1 2 3 4 5 6 7 -1 x-axis -2 -3

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**You have seen that the equation 2x+3y =6 is giving a straight line in the graph**

Note: Solutions of an equation 2x + 3y =6 are x =0 , y=2 and x=3 , y=0. In any equation of the type ax + by+ c = 0 where a, b, c --- constants x , y variables will gives straight line in the graph These types of the equations are called LINEAR EQUATIONS

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**If in an equation ax+ by + c= 0**

Case1: When a =0,b= 0, then 0x + by +c = 0 e.g. in an equation 2x+3y =6 , If a=0 0x + 3y =6 3y = 6 –0x y =6-0x 3 x 1 2 -3 y

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**Let us plot the ordered pairs:**

(-3,2) (1,2) (2,2) Show me Show me Show me Y- axis LINE IS PARALLEL TO X-AXIS 3 0x+3y =6 * 2 * * (-3,2) (1,2) (2,2) 1 -3 -2 -1 1 2 3 4 5 6 7 -1 x-axis -2 -3

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Case2: if in an equation ax+ by + c= 0 when a =0, b =0, then ax + 0y + c =0 e.g. in an equation 2x+0y =6 , when b=0 2x + 0y =6 2x = 6 – 0y x =6-0y 2 x 3 y -2 1

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**Let us plot the ordered pairs: (3,3) (3,-2) (3,1)**

Show me Show me Show me Y- axis LINE IS PARALLEL TO Y-AXIS 3 2x +0y =6 * (3,3) 2 (3,1) * 1 -3 -2 -1 1 2 3 4 5 6 7 -1 x-axis -2 (3,-2) * -3

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**if in an equation ax+ by + c= 0 when**

Case3: When a =0,b= 0, c =0 ax +by = 0 e.g. in an equation 2x+3y =6 , if c=0 2x + 3y =0 2x = -3y x =-3y 2 x -3 3 y 2 -2

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**Let us plot the ordered pairs: (0,0) (-3,2) (3,-2)**

Show me Show me (3,-2) Show me Show me Y- axis LINE PASSES THROUGH THE CENTER 3 (-3,2) * 2 1 (0,0) * -3 -2 -1 1 2 3 4 5 6 7 -1 x-axis (3,-2) -2 * -3 2x+3y =0

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**If we draw two linear equations in one graph then we have three possibilities:**

one solution 1: Intersecting lines * 2: Parallel lines no solution 3. Lines will coincide many solutions

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**Now there is an exercise for you.**

Take any two linear equations. Plot them on the graph and observe what type of solution you get.

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**Mr. V.K. Sodhi ,Senior Lecturer,S.C.E.R.T.**

ACKOWLEDGEMENT Mr. V.K. Sodhi ,Senior Lecturer,S.C.E.R.T. “Mathematics” by R.S.AGGARWAL N.C.E.R.T. BOOK FOR Mathematics for Class-X Internet sites:

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Systems of Linear Equations in Two Variables. We have seen that all equations in the form Ax + By = C are straight lines when graphed. Two such equations,

Systems of Linear Equations in Two Variables. We have seen that all equations in the form Ax + By = C are straight lines when graphed. Two such equations,

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