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## LINEAR EQUATIONS

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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**Target group**Class ninth and tenth**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.**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”**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**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.**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.**2 kg**5 kg How much weight should be added to equalize the balance? + 2 kg = 5 kg**+ 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’**So we can say,**ax+b = 0 is an equation in one variable x Where a,b are constants & a = 0**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 (3, 0) (0,2) Ordered pairs**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) * 0 -3 -2 -1 1 2 3 4 5 6 7 -1 x-axis -2 -3**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**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**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 0 -3 -2 -1 1 2 3 4 5 6 7 -1 x-axis -2 -3**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**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 2x +0y =6 3 * (3,3) 2 (3,1) * 1 0 -3 -2 -1 1 2 3 4 5 6 7 -1 x-axis -2 (3,-2) * -3**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**Let us plot the ordered pairs:**(0,0) (-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) * 0 -3 -2 -1 1 2 3 4 5 6 7 -1 x-axis (3,-2) -2 * -3 2x+3y =0**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**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.**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: www.math.nice.edu www.math.org.uk www.pass.math.org.uk