3 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.
4 WHEN we talk to each other, we use sentences. What do we say?Either we talk or we give some statementsThese statements may be RIGHT or WRONGFor example we make the statement-”sunrises in the east and sets in the west”
7 WHEN we talk to each other, we use sentences. What do we say?Either we talk or we give some statementsThese statements may be RIGHT or WRONGFor example we make the statement-”sunrises in east and sets in west”This is a TRUE statementIt 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
8 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.
9 In mathematics, we often use OPEN STATEMENTS For example the statement ,“ any number added to 5 will give 8” is an open statementIf we add any number to 5, we may or may not get 85 + 1= 8FALSE STATEMENTFALSE STATEMENT5 + 2 = 85 + 3 = 8TRUE STATEMENTThe number 3 makes both the sides equal. Hence the statement becomes TRUE.
10 How much weight should be added to equalize the balance? 2 kg5 kgHow much weight should be added to equalize the balance?+ 2 kg = 5 kg
11 + 2kg = 5kgThe above statement becomesx+ 2= 5This statement is called an EQUATIONThis equation will be true depending on the value of the variable ‘x’
12 So we can say,ax+b = 0is an equation in one variable xWhere a,b are constants & a =
13 Let us take an example from daily life. Cost of two rubbers and three pencils is six rupeesIn mathematical form, it can be written as2x + 3y = 6,where x is the cost of one rubber and y of one pencilx3y2(3, 0)(0,2)Ordered pairs
14 Let us plot the ordered pairs: (3,0)Show me(0,2)Show meY- axis3(0,2)2*2x + 3y =61(3,0)*-3-2-11234567-1x-axis-2-3
15 You have seen that the equation 2x+3y =6 is giving a straight line in the graph Note:Solutions of an equation 2x + 3y =6are x =0 , y=2 and x=3 , y=0.In any equation of the type ax + by+ c = 0where a, b, c --- constantsx , y variableswill gives straight line in the graphThese types of the equations are called LINEAR EQUATIONS
16 If in an equation ax+ by + c= 0 Case1:When a =0,b= 0, then0x + by +c = 0e.g. in an equation 2x+3y =6 ,If a=00x + 3y =63y = 6 –0xy =6-0x3x12-3y
17 Let us plot the ordered pairs: (-3,2)(1,2)(2,2)Show meShow meShow meY- axisLINE IS PARALLEL TO X-AXIS30x+3y =6*2**(-3,2)(1,2)(2,2)1-3-2-11234567-1x-axis-2-3
18 Case2:if in an equation ax+ by + c= 0when a =0, b =0, thenax + 0y + c =0e.g. in an equation 2x+0y =6 ,when b=02x + 0y =62x = 6 – 0yx =6-0y2x3y-21
19 Let us plot the ordered pairs: (3,3) (3,-2) (3,1) Show meShow meShow meY- axisLINE IS PARALLEL TO Y-AXIS32x +0y =6*(3,3)2(3,1)*1-3-2-11234567-1x-axis-2(3,-2)*-3
20 if in an equation ax+ by + c= 0 when Case3:When a =0,b= 0, c =0ax +by = 0e.g. in an equation 2x+3y =6 , if c=02x + 3y =02x = -3yx =-3y2x-33y2-2
21 Let us plot the ordered pairs: (0,0) (-3,2) (3,-2) Show meShow me(3,-2)Show meShow meY- axisLINE PASSES THROUGH THE CENTER3(-3,2)*21(0,0)*-3-2-11234567-1x-axis(3,-2)-2*-32x+3y =0
22 If we draw two linear equations in one graph then we have three possibilities: one solution1: Intersecting lines*2: Parallel linesno solution3. Lines will coincidemany solutions
23 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.
24 Mr. V.K. Sodhi ,Senior Lecturer,S.C.E.R.T. ACKOWLEDGEMENTMr. V.K. Sodhi ,Senior Lecturer,S.C.E.R.T.“Mathematics” by R.S.AGGARWALN.C.E.R.T. BOOK FOR Mathematics for Class-XInternet sites: