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The system of equations 3x + y - 4 = 0 and 6x + 2y - 8 = 0 has
A) a unique solution x = 1, y=1
B) a unique solution x = 0, y = 4
C) no solution
D) infinite solutions
Correct answer:
D) infinite solutions
Description for Correct answer:
Given equations of system
3x + y = 4 ...(i)
6x + 2y = 8 ...(ii)
Here, \( \Large a_{1}=3, b_{1}=1, c_{1}=4, \)
\( \Large a_{2}=6, b_{2}=2, c_{2}=8 \)
Because, \( \Large \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{2} \)
So, the system of equations has infinite solutions, because it represents a parallel line.
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