Question
Do the following pair of linear equations have no solution? Justify your answer:x = 2y, y = 2x
✓
Answer
The system of linear equations has no solution if $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
x - 2y = 0 and 2x - y = 0
Here, $\frac{\text{a}_1}{\text{a}_1}=\frac{1}{2}$
and $\frac{\text{b}_1}{\text{b}_2}=\frac{-2}{-1}=2$
So, the given system of linear equations does not satisfy $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$.
x - 2y = 0 and 2x - y = 0
Here, $\frac{\text{a}_1}{\text{a}_1}=\frac{1}{2}$
and $\frac{\text{b}_1}{\text{b}_2}=\frac{-2}{-1}=2$
So, the given system of linear equations does not satisfy $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$.
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