# Linear Equations In Two Variables

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When the equation is in the form ax + by + c = 0, where a , b , c are real numbers and a and b both are non zero then it is called Linear equation in two variables x and y. The Solution will include an ordered pair of real numbers which satisfy both the equations.

5x - 7y = 12

x – 4y = 5

From the System of Linear Equations in Two variables x and y.

Example 1:

5x - 7y = 12                  equation 1

x – 4y = 5                     equation 2

This system of equation can be solved using Substitution method. Let us follow the example to understand better.

Solution:

From  equation 2 we get x = 4 y + 5

Substitute x in   Eq 1  5 * ( 4y+ 5 ) – 7 y = 12

20y – 7y = 12 – 25

So y = -1

Now we plug in  y to get x

x = 4y + 5 = 4 (-1) + 5 = 1

x = 1 ; y = -1

Example 2

4x – 2 y = 6            equation 1

3x + 4y = 10           equation 2

This system of equation can be solved using Elimination method. Let us follow the example.

Solution:

In the first step we do equation 1 times 3

12x – 6 y = 18

In the second step we do equation 2 times 4

12x + 16 y = 40

On  subtracting we get - 22y = -22

y =1.

We plug in y to find x  so x = 2

x =  2 ; y = 1