If the pair of linear equations x + 2y - 4 = 0 and 2x + 4y - 12 = 0 are plotted graphically, we get _____ solution(s).
A
one
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B
infinite number of
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C
zero
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D
three
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Solution
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.