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