Certainly! Let's solve the given problem step-by-step.
We are given the following equations:
1. [tex]\( 6 + x + y = 20 \)[/tex]
2. [tex]\( x + y = k \)[/tex]
Let's analyze the problem:
From equation 1:
[tex]\[ 6 + x + y = 20 \][/tex]
We need to isolate [tex]\( x + y \)[/tex]:
[tex]\[ x + y = 20 - 6 \][/tex]
So,
[tex]\[ x + y = 14 \][/tex]
Now, from equation 2 we know:
[tex]\[ x + y = k \][/tex]
Given both expressions for [tex]\( x + y \)[/tex], we can equate them:
[tex]\[ k = 14 \][/tex]
To find [tex]\( 20 - k \)[/tex], we substitute [tex]\( k \)[/tex] with 14:
[tex]\[ 20 - k = 20 - 14 \][/tex]
Therefore,
[tex]\[ 20 - k = 6 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{6} \][/tex]
