Question

On comparing the ratios of the coefficients, find out whether the pair of
equations x - 2y =0 and 3x + 4y -20 =0 is consistent or inconsistent​

Answer 1

Answer :

Consistent

Note:

★ A linear equation is two variables represent a straight line .

★ The word consistent is used for the system of equations which consists any solution .

★ The word inconsistent is used for the system of equations which doesn't consists any solution .

★ Solution of a system of equations : It refers to the possibile values of the variable which satisfy all the equations in the given system .

★ A pair of linear equations are said to be consistent if their graph ( Straight line ) either intersect or coincide each other .

★ A pair of linear equations are said to be inconsistent if their graph ( Straight line ) are parallel .

★ If we consider equations of two straight line

ax + by + c = 0 and a'x + b'y + c' = 0 , then ;

• The lines are intersecting if a/a' ≠ b/b' .

→ In this case , unique solution is found .

• The lines are coincident if a/a' = b/b' = c/c' .

→ In this case , infinitely many solutions are found .

• The lines are parallel if a/a' = b/b' ≠ c/c' .

→ In this case , no solution is found .

Solution :

Here ,

The given equations of lines are :

x - 2y = 0

3x + 4y - 20 = 0

Clearly , we have ;

a = 1

a' = 3

b = -2

b' = 4

c = 0

c' = -20

Now ,

a/a' = 1/3

b/b' = -2/4 = -1/2

c/c' = 0/-20 = 0

Clearly ,

a/a' ≠ b/b'

Thus ,

The given lines are interesting and hence the system is consistent .