Question

Given 3x – 5y – 8 =0, write another linear equation so that the lines represented by the pair are parallel / inconsistent?

Answer 1

FINAL ANSWER:-

$6x-10y-15=0$

THINGS TO KNOW:-

inconsistent line is  $\frac{a1}{a2} =\frac{b1}{b2} \neq \frac{c1}{c2}$

$a1x+b1y+c1=0\\a2x+b2y+c2=0$

GIVEN:-

$3x-5y-8 =0$ is the equation given

TO FIND:-

another linear equation so that the lines represented by the pair are parallel / inconsistent

SOLUTION:-

$3x-5y-8 =0$ is the equation

condition of equation for parallel or inconsistent line is  $\frac{a1}{a2} =\frac{b1}{b2} \neq \frac{c1}{c2}$

here another equation could be $6x-10y-15=0$

here

$a1=3\:\:\:\:a2=6\\b1=-5\:\:\:\:b2=-10\\c1=-8\:\:\:\:c2=-15$

now let's put in   $\frac{a1}{a2} =\frac{b1}{b2} \neq \frac{c1}{c2}$

we get

$\frac{3}{6} =\frac{-5}{-10} \neq \frac{-8}{-15}$

$\frac{1}{2}= \frac{1}{2} \neq \frac{8}{15}$   [←after simplifying]

hence  $6x-10y-15=0$ is another linear equation so that the lines ($3x-5y-8 =0$  and  

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Answer 2

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