Question
Lines š„ x and š¦ y are parallel. If š¶ = 11 š„ + 16 , š¹ = 7 š„ + 24 C=11x+16, F=7x+24 and š· = 4 š¦ + 18 D=4y+18 then find the values of š¶ C and š· D .
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GPT-4o mini
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:
\[
C = 27, \quad D = 22.
\]
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:
\[
C = 27, \quad D = 22.
\]
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