Question

Check whether the following pairs of linear equations are consistent or inconsistent: (1)x+ 2y = 10: 2x - 3y = 12 1 (2) 2x + 3y = 6; 4x + 6y = 12 (3) 3x + 5y = 30; 9x + 154​

Answer 1

Answer:

Step-by-step explanation:

1) Given that,

x + 2y = 10 and 2x - 3y = 12.

x + 2y - 10 = 0 and 2x - 3y - 12 = 0

a1/ a2 = 1 / 2 , b1 / b2 = 2 / - 3 , c1 / c2 = - 10 / - 12 = 5 / 6

Since, a1 / a2 ≠ b1 / b2 .

∴ They are intersecting lines and hence, consistent pair of linear equations.

2) Given that,

2x + 3y = 6 and 4x + 6y = 12

2x + 3y - 6 = 0 and 4x + 6y - 12 = 0.

a1 / a2 = 2 / 4 , b1 / b2 = 3 / 6 , c1 / c2 = - 6 / - 12 .

Since, a1 / a2 = b1 / b2 = c1 / c2.

∴ They are coincident lines ( dependent lines ).

3) Given that,

3x + 5y = 30 and 9x + 15y = 4.

3x + 5y - 30 = 0 and 9x + 15y - 4 = 0.

a1 / a2 = 3 / 9 , b1 / b2 = 5 / 15 , c1 / c2 = - 30 / - 4

Since, a1 / a2 = b1 / b2 ≠ c1 / c2.

∴ They are parallel lines and hence inconsistent papair of linear equations.

Answer 2

Step-by-step explanation:

Check whether the following pairs of linear equations are consistent or inconsistent : -

(1) x + 2y = 10; 2x - 3y = 12

(2) 2x + 3y = 6; 4x + y = 12

(3)3x + 5y= 30; 9x + 15y =