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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
Are the following pair of linear equations consistent? Justify your answer:
$\frac{3}{5}\text{x}-\text{y}=\frac{1}{2}$ and $\frac{1}{5}\text{x}-3\text{y}=\frac{1}{6}$
✓

Answer

For consistent system of linear equations $\text{a},\text{ b}\neq0$
$\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}$ (infinitely many solutions)
$\frac{\text{a}_1}{\text{a}_2}\neq\frac{\text{b}_1}{\text{b}_2}$ (unique solurion)
$\frac{3}{5}\text{x}-\text{y}=\frac{1}{2}$ and $\frac{1}{5}\text{x}-3\text{y}=\frac{1}{6}$
Here, $\frac{\text{a}_1}{\text{a}_2}=\frac{\frac{3}{5}}{\frac{1}{5}}=3$, $\frac{\text{b}_1}{\text{b}_2}=\frac{-1}{-3}=\frac{1}{3}$ and $\frac{\text{c}_1}{\text{c}_2}=\frac{\frac{1}{2}}{\frac{1}{6}}=\frac{6}{2}=3$
$\therefore\ \frac{\text{a}_1}{\text{a}_2}\neq\frac{\text{b}_1}{\text{b}_2}$
So, the givne pair of linear equations is consistent and has unique solution.

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