Question

If the pair of linear equations $\text{x + 2y - 4 = 0}$ and $\text{2x + 4y - 12 = 0}$ are plotted graphically, we get _____ solution(s).

• A. one
• B. infinite number of
• C. zero
• D. three

Answer 1

The correct option is C zero

Equation 1:
x + 2y - 4 = 0
x + 2y = 4
When x = 0, 2y = 4 $⟹$ y = 2
When x = 4, 4 + 2y = 4 $⟹$ y = 0

Equation 2:
2x + 4y = 12
When x = 0, 4y = 12 $⟹$ y = 3
When x = 6, 12 + 4y = 12 $⟹$ y = 0

Plotting the linear equation graphically:

This shows that both the linear equations are parallel to each other. Thus, there is no solution for x and y.