# Linear Equation in Two Variables

Hello students, Previously we have discussed about slope worksheet and today I am going to discuss about **Linear Equation in Two Variables**. A equation of the form ax + by + c = 0 where a, b, c are real numbers is called a linear equation in two variables x and y.

Let us see some **Linear Equation in Two Variables examples**.

Example :- show that x=3 and y= 2 in the equation of 5x – 3y = 9

Solution:-

step1:- put x=3 and y=2 in the given equation, we get

step 2:- L.H.S =5*3-3*2 = 9(R.H.S)

step 3:- 15 – 6 = 9(R.H.S)

step 4:-so, x=3 and y=2 is a solution of 5x-3y=9

step 5:- L.H.S=R.H.S

Now, we will discuss about simultaneous linear equations in two variables.

Two linear equation in unknown variables x and y are said to form a system of simultaneous linear equations if each of them gets satisfied by the same pair of values of x and y.

Example:- show that x=5, y=2 is a solution of the system of linear equations.2x + 3y = 16, x – 2y = 1

Solution:-

step 1:- the given equations are:-

2x +3y =16

x-2y =1

step 2:- putting x =5, y =2 in eq.(1) we get:

L.H.S= (2*5+3*2)=16=(R.H.S)

Step 3:-putting x =5, y =2 in eq.(2) we get:

L.H.S= (5-2*2)=1=(R.H.S)

so, x=5, y=2 satisfy both eq(1) and eq(2). It is a solution of the given system of equations.

Now, we will talk about consistent and inconsistent systems of linear equations in two variables.

First one is consistent system of linear equation . A system of two linear equations in two unknown variables is said to be consistent if it has at least one solution.

Second one is inconsistent system of linear equation. A system of two linear equations in two unknown is said to be inconsistent if it has no solution at all.

Example:- Find whether the system of linear equations. x + y = 3, 2x +2y = 7 is consistent or inconsistent system of linear equations.

solution:-The given system is inconsistent because we cannot find values of x and y which may satisfy both the given equations simultaneously.

In the next session we will discuss about Math Blog on Graphing Linear Equations with One Variable and You can visit our website for getting information about Precalculus Help and cbse question papers 2011 class x.

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