Question

The system of equations 6x+3y=c-3 and 12x+cy=c has infinitely many solution then the value of C will be

Answer 1

Hi,

Here is your answer

Given:

6x+3y=c-3

12x+cy=c

To Find:

The value of c

Solution:

Since the equation has infinite number of solutions,

$\frac{a1}{a2} =\frac{b1}{b2} =\frac{c1}{c2}$

where a1=6,a2=12,b1=3,b2=c,c1=c-3,c2=c

Substituting the datas in the above equation

We get,

$\frac{6}{12} =\frac{3}{c} =\frac{c-3}{c}$

Hence from the first part

6c=36

c=6

From the second part

c²-3c=3c

c²=6c

c=6

Hence the value of c=6

Notes:

1. If a pair of equations has a unique solution,

$\frac{a1}{a2} \neq \frac{b1}{b2}$

2. If a pair of equations has infinite solutions,

$\frac{a1}{a2} =\frac{b1}{b2} =\frac{c1}{c2}$

3. If a pair of equations has no solution,

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

Hope this helps you.

Answer 2

c=》6 is the answer.

hope it helps you