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Pair of Linear Equations in Two variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsPair of Linear Equations in Two variables1 Mark
Question
Do the following equations represent a pair of coincident lines? Justify your answer:
$\frac{\text{x}}{2}+\text{y}+\frac{2}{5}=0$ and $4\text{x}+8\text{y}+\frac{5}{16}=0$
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Answer

Condition for coincident lines $\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}\ .....(\text{i})$
$\frac{\text{x}}{2}+\text{y}+\frac{2}{5}=0$ and $4\text{x}+8\text{y}+\frac{5}{16}=0$
Here, $\frac{\text{a}_1}{\text{a}_2}=\frac{\frac{1}{2}}{8}=\frac{1}{8}$, $\frac{\text{b}_1}{\text{b}_2}=\frac{1}{8}$ and $\frac{\text{c}_1}{\text{c}_2}=\frac{\frac{2}{5}}{\frac{5}{16}}=\frac{32}{25}$
$\therefore\ \frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
So, the given system of linear equations does not satisfy condition (i).

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