Question

if 2a+3b-c=0 and a-2b+2c=0
then
a)a:b:c=4:7:5
b) a:b:c=5:7:-4
c)a:b:c=-4:5:7
d) a:b:c=-4:5:-7​

Answer 1

Concept:

Here, we have applied the concept of addition, multiplication, and subtraction.

Given:

Two equations are given to us

$2a+3b-c=0\\ a-2b+2c=0$

To find:

We have to find the ratio between a, b, and c.

Solution:

In this question, two equations are given to us,

$2a+3b-c=0 \\a-2b+2c=0$....1 and 2

Now, we have to find the ratio between a, b, and c.

So, first, we will multiply 2 in equation 1

On multiplying 2 in equation 1, we get

$2a+3b-c*2\\4a+6b-2c=0$......3

Now, we will add equation 2 to equation 3

So, we get

$4a+6b-2c+a-2b+2c\\5a+4b=0$.....4

So from equation 4, we get,

$5a+4b=0\\\frac{a}{b} =\frac{4}{5} \\a:b=4:5$

Now, we will multiply equation 2 by 2

$a-2b+2c*2\\2a-4b+4c$.....5

So, now will subtract equation 1 to equation 5 and we get

$2a-4b+4c-2a+3b-c\\7b-5c$.....6

So, from equation 6 we get

$7b-5c=0\\\frac{b}{c} = \frac{-5}{-7} \\b:c= -5: -7$

∴ From above we get, a=4, b= -5, and c= -7

a= -4, b= 5, c= 7

So, a:b:c= -4:5:7

Hence, option c is correct.

#SPJ2