Question

Draw graph of x - 2y = 4 , 2x - 4y = 12 on the same co-ordinate plane. Observe it,. Think of the relation between the coefficients of x , coefficients of y and the constant terms and draw the inference.

Answer 1

Solution:

The two linear equation in two variable are

1.x- 2 y=4

2. 2 x - 4 y=12

So, if two lines are parallel then their slopes are equal

And , if they are coincident , Line 1= K × Line 2 , or Line 2= P × Line 1, where P and K are any real number.

But if you will observe the two lines

2×Line 1= 2 x - 4 y-8≠Line 1=2 x - 4 y-12

So, these two lines are not coincident.

Now, Line 1 can be written as, 2 y= x -4

Line , 2 can be written as

4 y=2 x -12

Comparing with slope intercept form of line, y= m x + c

Slope of line 1

Slope of line 2

→→As, slopes are equal. So, these two lines are Parallel.Also,

→Coefficient of x of line 2 = 2 × Coefficient of x of line 1

→Coefficient of y of line 2=2× Coefficient of y of line 2