Question

Which one of the following graphs is consistent and dependent?

• A. 2x + 3y = 15; 4x + 7y = 11
• B. 4x + y = 12; 8x + 2y = 24
• C. x + 2y = 5; 2x + 4y = 15
• D. 11y + 3x = 1; 5y + 2x = 7

Answer 1

The correct option is B 4x + y = 12; 8x + 2y = 24

A pair of linear equations in two variables is said to be consistent and dependent if a consistent system has an infinite number of solutions.
Now, plot the line 4x + y = 12
At x = 0$⟹$ y = 12
At y = 0$⟹$ x = 3

So, the line passes through (0,12) and (3,0).

Plot the line 8x + 2y = 24
At x = 0$⟹$ y = 12
At y = 0$⟹$ x = 3

So, the line passes through (0,12) and (3,0).
Here, the above lines overlap each other. So, they have infinte number of solutions.

Hence, the two lines are consistent and dependent.