Question

Lines x and y are parallel. If B=5x+8,G=1x+24 and H=4y+20 then find the values of x and y.

Answer 1

Y is wrong

Answer 2

To find the values of \( x \) and \( y \) given that lines \( x \) and \( y \) are parallel, we need to use the property that corresponding angles formed by a transversal intersecting two parallel lines are equal.

From the equations given:

1. \( B = 5x + 8 \)
2. \( G = 1x + 24 \)
3. \( H = 4y + 20 \)

Since lines \( x \) and \( y \) are parallel, we can set angles \( B \) and \( G \) equal to each other:

\[
5x + 8 = 1x + 24
\]

Now we'll solve for \( x \):

1. Subtract \( 1x \) from both sides:
\[
5x - 1x + 8 = 24
\]
\[
4x + 8 = 24
\]

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

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

Next, we need to find \( y \). Since we don't have a direct relationship given between \( H \) and \( G \), we will assume \( H \) is related to \( G \) (i.e., they could represent another set of corresponding angles). We already know the relationship between \( G \) and \( H \) should also adhere to the parallel line property.

Let's try equating the expressions for \( H \) using the found value of \( y \) related to a similar equation. Theoretically, we can assume \( H = G \):

\[
H = G \quad \Rightarrow \quad 4y + 20 = 1x + 24
\]
Substituting \( x = 4 \):
\[
4y + 20 = 1(4) + 24
\]
\[
4y + 20 = 4 + 24
\]
\[
4y + 20 = 28
\]
Now, subtract 20:
\[
4y = 8
\]
Finally, divide by 4:
\[
y = 2
\]

Thus, the values of \( x \) and \( y \) are:

\[
x = 4, \quad y = 2
\]

Answer 3

Apologies for any confusion. Let's clarify the relationships more carefully based on your original equations and the fact that lines \( x \) and \( y \) are parallel.

1. **Equate angles \( B \) and \( G \)** since they are corresponding angles (if we assume they are corresponding angles):

\[
B = G \implies 5x + 8 = 1x + 24
\]

Now solving this equation step by step:

1. Subtract \( x \) from both sides:
\[
5x - x + 8 = 24
\]
\[
4x + 8 = 24
\]

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

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

Now we need to calculate \( H \). If lines \( x \) and \( y \) are parallel, and \( H \) is corresponding to an angle either from the situation not explicitly stated, we need to equate \( G \) to \( H \).

Assuming \( G \) and \( H \) are also corresponding angles, we set:

\[
G = H \implies 1x + 24 = 4y + 20
\]

Substituting \( x = 4 \):

\[
1(4) + 24 = 4y + 20
\]
\[
4 + 24 = 4y + 20
\]
\[
28 = 4y + 20
\]
Subtracting 20 from both sides gives:

\[
8 = 4y
\]

Now divide by 4:

\[
y = 2
\]

Thus, the values for \( x \) and \( y \) are:

\[
x = 4, \quad y = 2
\]

If the conditions of the problem should be different or if \( H \) needs to relate to something else, please provide that context, and I can adjust the calculation accordingly.