Question

Find the ratio a : b : c if a + 2b - c = 0 & 2a - b + c = 0 .

Answer 1

Answer:

${\bf{\green{=>a+2b-c=0..EQ1}}}$

${\bf{\red{=>2a-b+c=0..EQ2}}}$

${\bf{\blue{adding }}}$${\bf{\blue{EQ1}}}$${\bf{\blue{and}}}$${\bf{\blue{EQ2}}}$

${\bf{\orange{=>a+2b-c+2a-b+c=0}}}$

${\bf{\red{=>3a+b=0}}}$

${\bf{\green{=>b=-3a..EQ3}}}$

${\bf{\green{Sub}}}$${\bf{\red{'b' }}}$${\bf{\blue{value}}}$${\bf{\pink{in}}}$${\bf{\green{EQ1}}}$

${\bf{\orange{=>a+2b-c=0}}}$

${\bf{\blue{=>a+2(-3a)-c=0}}}$

${\bf{\red{=>a-6a-c=0}}}$

${\bf{\green{=>-5a-c=0}}}$

${\bf{\pink{=>5a+c=0}}}$

${\bf{\green{=>c=-5a..EQ4}}}$

${\bf{\red{Sub}}}$${\bf{\blue{EQ3}}}$${\bf{\pink{and}}}$${\bf{\green{EQ4}}}$${\bf{\orange{in}}}$

M${\bf{\blue{EQ1}}}$

${\bf{\red{=>a+2(-3a)-(-5a)=0}}}$

${\bf{\green{=>a-6a+5a=0}}}$

${\bf{\pink{=>}}}$

${\bf{\blue{}}}$

${\bf{\red{}}}$

${\bf{\blue{}}}$

${\bf{\pink{}}}$

${\bf{\green{}}}$

${\bf{\orange{}}}$

${\bf{\blue{}}}$

${\bf{\red{}}}$

${\bf{\green{}}}$

${\bf{\pink{}}}$

${\bf{\blue{}}}[/tex</p><p></p><p>[tex]{\bf{\pink{}}}$

[tex]{\bf{\blue{}}}[/tex