Question

On comparing the ratios
1 1 1
2 2 2
, ,
a b c
a b c
and without
drawing them check, whether the system of
equations 9x + 8y – 15 = 0 and
40 15 25 0
3
x y   
intersect at a point, are parallel or coincide.

Answer 1

$Compare \: given \: simultaneous \: equations \\9x + 8y - 15 = 0 \: and \: 40x + 15y + 25 = 0 \:with\\a_{1}x + b_{1}y + c_{1} = 0 \:and \\a_{2}x + b_{2}y + c_{2} = 0, we \:get$

$a_{1} = 9 , \: b_{1} = 8 , \: c_{1} = -15 \: and\\a_{2} = 40 , \: b_{2} = 15 , \: c_{2} = 25$

$i) \frac{a_{1}}{a_{2}} = \frac{9}{40}$

$ii) \frac{b_{1}}{b_{2}} = \frac{8}{15}$

$\green {\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} }$

Therefore.,

$\blue { Above \: equations \: represents }\\\blue { \: intersecting \:lines }$

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