Graphically, find whether the following pair of equations has no … - Vidyadip

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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