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Linear Equations In Two Variables — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsLinear Equations In Two Variables2 Marks
Question
On comparing the ratios $\frac{\text{a}_1}{\text{a}_2},\frac{\text{b}_1}{\text{b}_2}$ and $\frac{\text{c}_1}{\text{c}_2},$ and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.
$6x - 3y + 10 = 0$
$2x - y + 9 = 0$
✓

Answer

Given equation are:
$6x - 3y + 10 = 0$
$2x - y + 9 = 0$
Where, $a_1 = 6, b_1 = -3, c_1= 10$
$a_2 = 2, b_2 = -1, c_3= 9$
We get $\frac{\text{a}_1}{\text{a}_2}=\frac{6}{2},\frac{\text{b}_1}{\text{b}_2}=\frac{-3}{-1}=\frac{\text{c}_1}{\text{c}_2}=\frac{10}{9}$
$\Rightarrow\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=3$
Thus the pair of line is parallel lines.

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