Скачать или смотреть Pair of Linear Equations in two variable EX-3.4 {part:-9} दो चर वाले रैखिक समीकरण NCERT Class 10th

This video is about Linear equation, linear equation in one variable, linear equation in two variables and one degree equation.

Q: What is linear equation?
Ans: Linear equation is defined as one degree equation which make a straight line on a graph. Or one can say that when the highest degree of an equation is one than we call of linear equation.

For example, 3x+4y= 8

In this equation there are three terms 3x, 4y and 8. Here in this equation "x" and "y" are variables while 8 is a constant, 3 is the coefficient of variable "x" and 4 is the coefficient of variable "y". The highest power of the variable "x" is one while the highest power of the variable "y" is also one. Hence, it is a one degree equation. Therefore, it is also known as linear equation.

Q: How to determine linear equation?
Ans: In order to determine a linear equation, look at the highest power of an equation. If the highest power of the equation is one, than it is a linear equation. If the highest power of the equation is not one or other than one like two or three, than it is not a linear equation.

For example, 2xy + 5 = 10

There are also three terms in this equation. The term "2xy" is considered as one term. The power of the variable "x" is one while the power of the variable "y" is also one hence, one plus one is equal to two. Thus the highest power of this equation is two. Therefore, it is neither one degree equation, nor a linear equation.

Q: How to calculate or find the value of linear equation in one variable?
Ans: In order to calculate the value of linear equation, we have to do some algebraic operations.

For example, 2x + 20 = 50

We know that the left hand side of the equality sign is known as L.H.S and the right side of the equality sign is known as R.H.S. Hence, we will shift "+20" from the L.H.S to the R.H.S. As a result, the positive sign of the "+20" will be changed into the negative sign. Thus, we will get:

2x = 50 - 20
2x = 30
Now dividing both sides of the equation by "2". As a result, we will get "x = 15" . Thus the value of the variable "x" is 15.

Q: How can we solve a linear equation in two variables?
Ans: There are different methods of solving linear equation in two variables, but we will solve a linear equation in two variables by adding equation one and equation two. After that, we will get the value of one variable and than we will put the value of that variable in the second equation also known as substitution method in order to get the value of second variable.

For example, x + y = 8 .... Equation One
X - y = 6 .... Equation Two
Now we will add equation one and equation two, as a result variable "y" will be cancelled out. We will get "2x = 14". So we will divide both sides by 2. Hence, we will get "x=7". Now we can put the value of "x" in either equation one or in equation two. For instance, we put the value of "x=7" in equation one. We get:
7 + y = 8
y = 8 - 7
y = 1
Thus, we successfully solve the linear equation in two variables where the value of variable "x=7" while the value of variable "y=1".

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