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# Pair of linear equation in two variable

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### Pair of linear equation in two variable

1. 1. PAIR OF LINEAR EQUATION IN TWO VARIABLE EFFORTS BY: ARPIT MATHUR CLASS: XC
2. 2. WHAT IS LINEAR EQUATION? An equation between two variables that gives a straight line when plotted on a graph.
3. 3. WHAT IS LINEAR EQUATION IN TWO VARIABLE? A linear equation in two variables is an equation with two variables (usually called x and y) where the variables are at most multiplied by a number, and added to something else. No exponents, no variables in denominators, no fancy functions of the variables. For example 2x-y=3 and x+y=3 are linear equations.
4. 4. GRAPH OF LINEAR EQUATION IN TWO VARIABLE
5. 5. TYPES OF SOLUTIONS OF SYSTEMS OF EQUATIONS • One solution – the lines cross at one point • No solution – the lines do not cross • Infinitely many solutions – the lines coincide
6. 6. A PAIR OF LINEAR EQUATIONS IN TWO VARIABLES CAN BE SOLVED BY THE: (I) GRAPHICALLY METHOD (II) ALGEBRAIC METHOD
7. 7. TO FIND THE VALUES OF X AND Y BY ALGEBRAIC METHOD THERE ARE THREE METHODS Substitution Method Elimination Method Cross-Multiplication Method We can also find the values of X and Y graphically by finding there co-ordinates and then plotting on the graph
8. 8. FINDING THE VALUES OF X AND Y BY GRAPHICAL METHOD • We can also find the values of X and Y graphically by finding there co-ordinates and then plotting on the graph
9. 9. SUBSTITUTION METHOD STEPS Obtain the two equations. Let the equations be a1x + b1y + c1 = 0 ----------- (i) a2x + b2y + c2 = 0 ----------- (ii) Choose either of the two equations, say (i) and find the value of one variable , say ‘y’ in terms of x Substitute the value of y, obtained in the previous step in equation (ii) to get an equation in x Solve the equation obtained in the previous step to get the value of x. Substitute the value of x and get the value of y.
10. 10. • The method of substitution is not preferable if none of the coefficients of x and y are 1 or -1. For example, substitution is not the preferred method for the system below: 2x – 7y = 3 -5x + 3y = 7 • A better method is elimination by addition. The following operations can be used to produce equivalent systems: • 1. Two equations can be interchanged. • 2. An equation can be multiplied by a non-zero constant. • 3. An equation can be multiplied by a non-zero constant and then added to another equation ELIMINATION METHOD
11. 11. CROSS-MULTIPLICATION METHOD • Let’s consider the general form of a pair of linear equations. 𝑎1 𝑥+𝑏1y+𝑐1=0 𝑎2 𝑥+𝑏2y+𝑐2=0 To solve this pair of equations for 𝑥 and 𝑦 using cross-multiplication, we’ll arrange the variables and their coefficients 𝑎1, 𝑎2 and 𝑏1, 𝑏2 and the constants 𝑐1, 𝑐2 We can convert non linear equations in to linear equation by a suitable substitution
12. 12. •Thank You