Question

Find values of c and d that satisfy each of the following equations. (There may be more than one correct answer.)

1. cd = 0
2. (c − 5)d = 2
3. (c − 5)d = 0
4. (c − 5)(d + 3) = 0

Answer 1

The given equations have no solution.

Explanation:

The given equations are

1. cd = 0

2. (c − 5)d = 2

3. (c − 5)d = 0

4. (c − 5)(d + 3) = 0

From the given equations it is clear that left side of equation (2) and (3) are same but right side of the equation are not same, which not possible for any values of c and d.

The second equation is

`(c-5)d=2`

Using equation (3), substitute the (c-5)d=0 in the above equation.

`0=2`

The above statement is false because we know that
`0\\eq 2`.

Therefore, the given system of equations have no solution.