Question

prove that the lines y=5×+7 and 2y=10×+5 are parallel​

Answer 1

Given :-

Two linear equations in two variables i.e y = 5x + 7 and 2y = 10x + 5

To Show :-

The graph of pair of linear equations shows parallel lines.

Used Concepts :-

• A general linear equation in two variables is in the form of " ax + by + c = 0 " .
• If given two Linear equation in two variable . So , If :-

1. a1/a2 = b1/b2 = c1/c2 . Then the graph of the lines of the equations are coincidence.
2. a1/a2 ≠ b1/b2 = c1/c2 . Then the graph of the lines of the equations are intersecting.
3. a1/a2 = b1/b2 ≠ c1/c2 . Then the graph of the lines of the equations are parallel.

Solution :-

Here , Equation 1 :- 5x + 7 = y

=> Rearranging , the equation in the form of general linear equation in two variables we get ,

5x - y + 7 = 0

a1 = 5 , b1 = -1 and c1 = 7

Equation 2 :- 10x + 5 = 2y

=> Again rearranging we get ,

10x - 2y + 5 = 0

a2 = 10 , b2 = -2 and c2 = 5

Here , a1/a2 = 5/10 = 1/2 ------( i )

b1/b2 = -1/-2 = 1/2 ------( ii )

c1/c2 = 7/5 ------( iii )

By , ( i ) , ( ii ) and ( iii ) ,

a1/a2 = b1/b2 ≠ c1/c2 .

Henceforth , The graph of the given linear equations shows parallel lines.