Question

Which of the following pairs of linear equations are consistent/inconsistent?
(i) x + 3y – 5 = 0, 2x + y = 0
(ii) 2x + y = 1, 2y = 2 – 4x
(iii) 2x – y = 2, 2y – 4x = 2

• A. Yes, No , No
• B. No,No,No
• C. Yes,Yes,Yes
• D. Yes,Yes,No

Answer 1

The correct option is D

Yes,Yes,No

Yes, No, No

(i) x + 3y – 5 = 0,
2x + y = 0

$\frac{1}{2}\ne \frac{3}{1}$
The pair of linear equations is consistent.

(ii) 2x + y = 1,
2y = 2 – 4x

$\frac{2}{4}=\frac{1}{2}=\frac{1}{2}$
The pair of linear equations is dependent and consistent.

(iii) 2x – y = 2,
2y – 4x = 2

$\frac{-2}{4}=\frac{-1}{2}\ne \frac{2}{2}$
The pair of linear equations is inconsistent.