LINEAR EQUATIONS

LINEAR EQUATIONS2x+ 3y =63x-4y =7-6x +7y = 42-9x - 4x = -365x 8y =-403x 7y =219x - 4x = -363x 7y =21Mrs. ChanderkantaMrs. Anju Mehta

Target groupClass ninth and tenth

LEARNING OBJECTIVESDefine 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 statementsThese statements may be RIGHT or WRONGFor 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 statementsThese statements may be RIGHT or WRONGFor example we make the statement- sunrises in east and sets in westThis 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

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, =R.H.S.L.H.S.

In mathematics, we often use OPEN STATEMENTS For example the statement ,If we add any number to 5, we may or may not get 8

5 + 1= 8 5 + 2 = 8 5 + 3 = 8The number 3 makes both the sides equal. Hence the statement becomes TRUE.

FALSE STATEMENT

FALSE STATEMENT

TRUE STATEMENT

any number added to 5 will give 8 is an open statement

5 kg2 kgHow much weight should be added to equalize the balance? + 2 kg = 5 kg

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

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

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

x 30 y02

Let us plot the ordered pairs:(3,0) x-axisY- axis 1 2 3 4 5 6 71-1-1 2 -2 -23-3-3**0 Show me(0,2)Show me2x + 3y =6(3,0) (0,2)

You have seen that the equation 2x+3y =6 is giving a straight line in the graphThese types of the equations are called LINEAR EQUATIONSSolutions 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 = 0where a, b, c --- constants x , y --- variableswill gives straight line in the graphNote:

If in an equation ax+ by + c= 0 Case1: When a =0,b= 0, then

e.g. in an equation 2x+3y =6 , 0x + 3y =63y = 6 0xy =6-0x 3If a=00x + by +c = 0

x12-3y222

Let us plot the ordered pairs: x-axisY- axis 1 2 3 4 5 6 71-1-1 2 -2 -23-3-30

***

(1,2) (2,2)(-3,2)(1,2)(2,2)(-3,2)Show meShow meShow me0x+3y =6LINE IS PARALLEL TO X-AXIS

if in an equation ax+ by + c= 0 Case2: when a =0, b =0, then

e.g. in an equation 2x+0y =6 , 2x + 0y =62x = 6 0yx =6-0y 2ax + 0y + c =0when b=0

x333y-213

Let us plot the ordered pairs:(3,-2) x-axisY- axis 1 2 3 4 5 6 71-1-1 2 -2 -23-3-30 (3,1)Show meShow me(3,3)***Show me(3,-2)(3,1)(3,3)2x +0y =6LINE IS PARALLEL TO Y-AXIS

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=02x + 3y =02x = -3yx =-3y 2

x-330y2-20

Let us plot the ordered pairs:(-3,2) x-axisY- axis 1 2 3 4 5 6 71-1-1 2 -2 -23-3-30 Show me(3,-2)Show meShow me(0,0)Show me***(-3,2)(3,-2)(0,0)2x+3y =0LINE PASSES THROUGH THE CENTER

If we draw two linear equations in one graph then we have three possibilities:1: Intersecting lines*one solution2: Parallel linesno solution3. Lines will coincidemany 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.

ACKOWLEDGEMENTMathematics by R.S.AGGARWALN.C.E.R.T. BOOK FOR Mathematics for Class-XMr. V.K. Sodhi ,Senior Lecturer,S.C.E.R.T.Internet sites:www.math.nice.eduwww.math.org.ukwww.pass.math.org.uk