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Linear Equations in Two Variables — Maths STD 10 — Question

CBSE 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.
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$
✓

Answer

Given equation are:
$5x - 4y + 8 = 0$
$7x + 6y - 9 = 0$
Where, $a_1 = 5, b_1 = -4, c_1= 8$
$a_2 = 7, b_2 = 6, c_3= -9$
We get $\frac{\text{a}_1}{\text{a}_2}=\frac{5}{7},\frac{\text{b}_1}{\text{b}_2}=\frac{-4}{6}=\frac{-2}{3}$
and $\frac{\text{c}_1}{\text{c}_2}=\frac{8}{-9}$
$\Rightarrow\frac{\text{a}_1}{\text{a}_2}\neq\frac{\text{b}_1}{\text{b}_2}$
Thus the pair of linear equation is intersecting.

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