PAIR OF LINEAR EQUATION IN TWO VARIABLE

EFFORTS BY: ARPIT MATHUR

CLASS: XC

WHAT IS LINEAR EQUATION?

An equation between two variables that gives a straight line when plotted on a graph.

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.

GRAPH OF LINEAR EQUATION IN TWO VARIABLE

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

A PAIR OF LINEAR EQUATIONS IN TWO VARIABLES CAN BE SOLVED BY THE:

(I) GRAPHICALLY METHOD

(II) ALGEBRAIC METHOD

TO FIND THE VALUES OF X AND Y BY ALGEBRAIC METHOD

THERE ARE THREE METHODSSubstitution MethodElimination MethodCross-Multiplication Method

We can also find the values of X and Y graphically by finding there co-ordinates and then plotting on the graph

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

SUBSTITUTION METHODSTEPS

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.

• 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

CROSS-MULTIPLICATION METHOD

• Let’s consider the general form of a pair of linear equations.

1++1=0 ++=0

To solve this pair of equations for and using cross-multiplication, we’ll arrange the variables and their coefficients

1, and , and the constants 1,

We can convert non linear equations in to linear equation by a suitable substitution

•Thank You