Question

Lines 𝑥 x and 𝑦 y are parallel. If 𝐶 = 11 𝑥 + 16 , 𝐹 = 7 𝑥 + 24 C=11x+16, F=7x+24 and 𝐷 = 4 𝑦 + 18 D=4y+18 then find the values of 𝐶 C and 𝐷 D .

Answer 1

Since lines \( x \) and \( y \) are parallel and are equations for lines, we can infer relationships based on their slopes.

From the given equations:

1. \( C = 11x + 16 \)
2. \( F = 7x + 24 \)
3. \( D = 4y + 18 \)

The slope of line \( C \) is 11, and the slope of line \( F \) is 7, while the slope of line \( D \) is 4.

However, since \( x \) and \( y \) are parallel, the values of \( C \) and \( D \) depend on the same \( x \) and \( y \) values maintaining the constant relationship.

### Finding Values of C and D

- \( C \) can be evaluated directly using its expression.
- To find \( D \) in terms of \( C \), observe that as lines parallel, the relationships of corresponding points will also vary by the same differences.

So let's call the \( x \) values the same for both equations \( C \) and \( D \), and consider the equations linearly.

1. For \( C \), simply substituting a value of \( x \):
- Let us suppose \( x = 1 \):
\[
C = 11(1) + 16 = 11 + 16 = 27
\]

2. To find \( D \), we need to express \( y \). Under the linearity of these functions and the factor dependencies, without losing generality, we can set \( y = 1 \) (as a typical representation):
Since the equations must be consistent, putting \( y = 1 \):
\[
D = 4(1) + 18 = 4 + 18 = 22
\]

### Results

- The calculated value of \( C \) is \( 27 \).
- The calculated value of \( D \) is \( 22 \).

Thus, the values are:
\[
C = 27, \quad D = 22.
\]