Question

If 2c+3b-c=0 and a-2b+2c=0 then a:b:c =?​

Answer 1

Answer:

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Answer 2

If $2c+3b-c=0$  and  $a-2b+2c=0$ then $a:b:c$  is $-4:5:7$ .

Step-by-step explanation:

We are given two equations,

$2a+3b-c=0$

$a-2b+2c=0$

and we have to find the ratio of $a:b:c$ .

• Calculation for ratio

we have two equations as  

$2a+3b-c=0$                ---(1)

$a-2b+2c=0$                  ---(2)  

we have to find the value of a, b and c to find the ratio.

We can find a, b and c by using Elimination method.

Extracting 'a' from equation (1)

$2a+3b-c=0$

$2a=c-3b$

$a=\frac{c-3b}{2}$

substitute this value of a in equation (2)  

 $a-2b+2c=0$

$\frac{c-3b}{2}-2b+2c=0$

$c-3b-2*2b+2*2c=0$

$c-3b-4b+4c=0$

$5c-7b=0$

$-7b=-5c$

$b=\frac{5c}{7}$

now substitute the value of b in extracted a,

$a=\frac{c-3b}{2}$

$a=\frac{c-3*(\frac{5}{7}c )}{2}$

   $=\frac{c-\frac{15}{7} c}{2}$

   $=\frac{\frac{7c-15c}{7} }{2}$

   $=\frac{7c-15c}{7*2}$

   $=\frac{-8c}{14}$

$a=\frac{-4c}{7}$

 now we have values of a and b in terms of c as,  

$a=\frac{-4c}{7}$   and   $b=\frac{5c}{7}$

the ratio is,

$a:b:c=\frac{-4c}{7} :\frac{5c}{7} :c$

            $=\frac{-4}{7} :\frac{5}{7} :1$

          $=-4:5:7$

In this way we get answer as ratio of  $a:b:c =-4:5:7.$