Question

Lines x and y are parallel. If
B=9x+16, F=5x+24 and H=2y+16 then find the values of x and y

Answer 1

2 is correct, but not 9

Answer 2

To find the values of \(x\) and \(y\) given the relationships in the problem, we need to use the fact that lines \(x\) and \(y\) are parallel. This condition implies that certain angles or relationships hold true.

From the expressions provided, we have:

- \(B = 9x + 16\)
- \(F = 5x + 24\)
- \(H = 2y + 16\)

It's not explicitly stated how \(B\), \(F\), and \(H\) are related, but since lines \(x\) and \(y\) are parallel, we can assume we need to set \(B\) equal to \(H\) or \(F\) equal to \(H\) or some other relation.

One common scenario with parallel lines is that their corresponding angles are equal. If we assume that \(B\) and \(F\) are corresponding angles related to parallel lines, we can set \(B\) = \(F\):

\[
9x + 16 = 5x + 24
\]

Now solve for \(x\):

1. Subtract \(5x\) from both sides:
\[
4x + 16 = 24
\]

2. Subtract 16 from both sides:
\[
4x = 8
\]

3. Divide by 4:
\[
x = 2
\]

Next, to find \(y\), we relate \(H\) back to either \(B\) or \(F\). Let's set \(H\) equal to \(B\):

\[
2y + 16 = 9x + 16
\]

Now substitute \(x = 2\):

\[
2y + 16 = 9(2) + 16
\]

This simplifies to:

\[
2y + 16 = 18 + 16
\]
\[
2y + 16 = 34
\]

Now solve for \(y\):

1. Subtract 16 from both sides:
\[
2y = 18
\]

2. Divide by 2:
\[
y = 9
\]

Thus, the final values are:

\[
x = 2, \quad y = 9
\]

Answer 3

Let's re-evaluate the second part of the problem, where we use \( H \) with the correct relation.

Given:

- \( B = 9x + 16 \)
- \( F = 5x + 24 \)
- \( H = 2y + 16 \)

We have found \( x = 2 \).

Now, we should correctly relate \( H \) to \( B \) or \( F \).

Let’s first calculate the value of \( B \) when \( x = 2 \):

\[
B = 9(2) + 16 = 18 + 16 = 34
\]

Now, let’s set \( H \) equal to \( B \):

\[
H = 2y + 16 = 34
\]

Now, solve for \( y \):

1. Subtract 16 from both sides:
\[
2y = 34 - 16
\]
\[
2y = 18
\]

2. Divide by 2:
\[
y = 9
\]

I see the confusion, but actually, \( y \) calculated as \( 9 \) is consistent with the calculations made.

If that’s not the correct answer, could you please clarify the relationships or how you’d like to find \( y \)? It's possible we may need a different step or a different equality based on the conditions of \( B \), \( F \), and \( H \).