1. Chapter :1
ïŽLinear Equation Using two
variables
Mrs Amrita Kulthe, Pune 1
Slides By:
Mrs. Amrita Kulthe
Secondary Teacher
Pune
2. E x p r e s s i o n
Mrs Amrita Kulthe, Pune
2
EXPRESSION
3. e.g. 2x+6=8
where a, b, and c are real numbers and . Linear Equations
are also first-degree equations because the exponent on the
variable is understood to be 1.
a, x, b, c, +, = ( đđ + đ = đ)
Linear equation using ONE variable
Mrs Amrita Kulthe, Pune 3
4. What is Linear Equation?
Linear Equations
A linear equation looks like any other equation. It is made up of two
expressions set equal to each other. A linear equation is special because:
It has one or two variables.
No variable in a linear equation is raised to a power greater than 1 or used
as the denominator of a fraction.
When you find pairs of values that make the linear equation true and plot
those pairs on a coordinate grid, all of the points for any one equation lie
on the same line. Linear equations graph as straight lines.
Mrs Amrita Kulthe, Pune 4
5.
6.
7. Here We will Learn General Form Of
Linear Equation using two variables..
đđ„ + đđŠ + đ = 0 âŠâŠWhere
1) a, b, and c are REAL NUMBERs
2) a â 0 , b â 0 at the same time⊠c is constant.
For e.g. đđ + đđ + đ = đ, đđ â đđ =9
Question Time:
Why we can not take both values zero at the
same time?
8.
9. SIMULTANEOUS EQUATION : -
Simultaneous equations are two equations,
each with the same two unknowns and are
"simultaneous" because they are solved
together.
Editor's Notes
While solving an equation, you must always keep the following points in mind:
The solution of a linear equation is not affected when:
The same number is added to (or subtracted from) both the sides of the equation.
You multiply or divide both the sides of the equation by the same non-zero number.
Let us now consider the following situation: In a One-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176 runs. Express this information in the form of an equation.
Here, you can see that the score of neither of them is known, i.e., there are two unknown quantities. Let us use x and y to denote them. So, the number of runs scored by one of the batsmen is x, and the number of runs scored by the other is y. We know that  x + y = 176 which is the required equation.
This is an example of a linear equation in two variables. It is customary to denote the variables in such equations by x and y, but other letters may also be used. Some examples of linear equations in two variables are:
You have seen that every linear equation in one variable has a unique solution.
When solving an equation, multiplying both sides of the equation by zero is not a good choice.
Multiplying both side of an equation by 0 will always result in an equation of 0 = 0, but an equation of 0 = 0 does not help you know what the solution to the original equation is.