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

CBSE BoardEnglish MediumSTD 10MathsPair of Linear Equations in Two variables2 Marks
Question
Graphically, find whether the following pair of equations has no solution, unique solution or infinitely many solutions:
5x - 8y + 1 = 0; ...(i)
3x - $\frac{24}{5}$y + $\frac{3}{5}$ = 0 ...(ii)
✓

Answer

$a_1 = 5,\ b_1 = -8,\ c_1 = 1$ and $a_2 = 3,\ b_2 =$ $\frac{-24}{5}$, $c_2 =$ $\frac{3}{5}$
$\frac { a _ { 1 } } { a _ { 2 } }$ = $\frac{5}{3}$ ...(i)
$\frac { b _ { 1 } } { b _ { 2 } }$ =$\frac { - 8 } { - 24 / 5 }$ = $\frac{5}{3}$ ...(ii)
and $\frac { c _ { 1 } } { c _ { 2 } }$ = $\frac { 1 } { 3 / 5 }$ = $\frac{5}{3}$ ...(iii)
Form (i), (ii) and (iii)
$\frac { a _ { 1 } } { a _ { 2 } } = \frac { b _ { 1 } } { b _ { 2 } } = \frac { c _ { 1 } } { c _ { 2 } }$
$\therefore$The pair of equations has infinitely many solutions.

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