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

CBSE BoardEnglish MediumSTD 10MathsPair of Linear Equations in Two variables5 Marks
Question
By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them:
$x – 2y = 6, 3x – 6y = 0$
✓

Answer

Given pair of equations is
$x - 2y = 6 .....(i)$
$3x - 6y = 0 .....(ii)$
On comparing With ax + by + c = 0, we get
$a_1 = 1, b_1 = -2$ and $c_1 = -6$ [from Eq. (i)]
$a_2 = 3, b_2 = -6$ and $c_2 = 0$ [from Eq. (ii)]
Here, $\frac{\text{a}_1}{\text{a}_2}=\frac{1}{3}$, $\frac{\text{b}_1}{\text{b}_2}=\frac{-2}{-6}$ and $\frac{\text{c}_1}{\text{c}_2}=\frac{-6}{0}$
$\therefore\ \frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
Hence, the lines represented by the given equations are parallel. Therefore, it has no solution. So, the given pair of lines in inconsistent.

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