Question

is really a family of equations, because for each value of k, we get a different equation with the unknown x. The letter k is called a parameter for this family. What value should we pick for k to make the given value of x a solution of the resulting equation

Answer 1

Follows are the solution to this question:

Explanation:

please find the complete question in the attached file:

In view of their choices, they could solve this problem by linking x and k finding values that meet the value.

a) In the family for equations they have, the plugin first x value.

`\to 3 * O +k-5=k * 0 -k+1 \\\\\to k-5 =-k+1 \\\\\to 2k =6 \\\\\to k= (6)/(2) \\\\`

`=3\\`

It is also obvious that k = 3 makes x = 0 for that equation family.

b) See now the second x value:

It is also obvious that k=3 renders a solution for this equation family of x=1.

c)

We plug in the 3rd of x, finally.

`\to 3 * 2 + k-5=k * 2-k+1 \\\to 6+ k-5= 2k-k+1 \\\to k+1= k+1 \\\to k-k= 1-1\\\ \ \ \ 0=0`

So k could be any real value and x=2 could be a solution for the equations family.

a) 3

b) 3

c) Any real value