9x-3y-12-0 0ex0ex18x-6y-24-0

Step 1: Compare both given equations 9x+3y+12=0 0ex0ex18x+6y+24=0with the general form of pair of linear equations a_1x + b_1y + c_1 = 0 0ex0exa_2x + b_2y + c_ ...

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Byju's Answer

Standard XII

Mathematics

Solving Homogeneous Differential Equations

9x+3y+12=0 0e...

Question

$9 x + 3 y + 12 = 0 18 x + 6 y + 24 = 0$

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Solution

Step 1: Compare both given equations $9 x + 3 y + 12 = 0 18 x + 6 y + 24 = 0$ with the general form of pair of linear equations $a_{1} x + b_{1} y + c_{1} = 0 a_{2} x + b_{2} y + c_{2} = 0$ in two variables
On comparing,
$a_{1} = 9, b_{1} = 3, c_{1} = 12 a_{2} = 18, b_{2} = 6, c_{2} = 24$
Step 2: Compare the ratios of $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}, a n d \frac{c_{1}}{c_{2}}$
$\frac{a_{1}}{a_{2}} = \frac{9}{18} = \frac{1}{2}$
$\frac{b_{1}}{b_{2}} = \frac{3}{6} = \frac{1}{2}$
$\frac{c_{1}}{c_{2}} = \frac{12}{24} = \frac{1}{2}$
On Comparing,
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ $= \frac{1}{2}$ ( If $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ then the pair of equation has $I n f i n i t e l y m a n y s o l u t i o n$ )
Hence, the given equation $9 x + 3 y + 12 = 0 18 x + 6 y + 24 = 0$ has $I n f i n i t e l y m a n y s o l u t i o n$

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