LINEAR EQUATIONS WITH TWO VARIABLES

THE EQUATIONS WITH TWO VARIBLES x AND y CALLED LINEAR EQUATIONS WITH TWO VARIABLES.

Solve the following system of linear equations:

{y=2x+4y=3x+2

Now from equation 1 put value of y in equation 2
we get
        y=3x+2
2x+4=3x+2
      4-2=3x-2x
         2=x
Hence x=2
Now putting value of x=2 in equation 1 we get,
y=2x+4
y=2*2+4
y=8

SOLUTION OF THESE TWO EQUATION  x=2 and y=8

 solutions of these two equations of straight line, solution of these two equations are inter section of line.

 Another example

 x+2y=1      ─⇀ 1

          2x-y = 3        ─⇀ 2

since the coefficient of x and y are both in these two equations
Multiply equation 2 with 2 so that the coefficient of y will be same
i.e.
 x+2y=1            ─⇀ 1
*2(2x-y)=3*2   ─⇀ 2

or

 x+2y=1            ─⇀ 1

4x-2y=6            ─⇀ 2

y=2x+4

y=2x+4

Now adding equation 1 and 2 we get
x+2y+4x-2y=1+6
                5x=7
                 x=7/5
And putting the value of x in equation 1 we get,
      x+2y=1
(7/5)+2y=1
           2y=1-(7/5)
           2y=(5-7)/2
               2y=-2/2
               y=(-1/2)

What is x,if 3x-2=4?
3x-2=4

3x=4+2

3x=6

x=2

or

3x-2=4

add +2 on both sides

3x-2+2=4+2

3x=6

x=2

y=3x+2

METHOD OF SOLVING: