Question

L is parallel to M, find the values of x and y in the equation (5y-23) / (2x+13) = 47 / (3x).

a) x = 5, y = 12
b) x = 3, y = 8
c) x = 7, y = 15
d) x = 4, y = 10

Answer 1

The values of x and y in the equation are x = 1 and y = 17.5. None of the provided options (a, b, c, d) match these values. None of the options are correct.

Step-by-step explanation:

To solve the given equation (5y-23) / (2x+13) = 47 / (3x) where L is parallel to M, we need to find the values of x and y.

First, set up a proportion by cross-multiplying:

(5y - 23)(3x) = (47)(2x + 13)

Simplify and expand:

15xy - 69x = 94x + 611

Combine like terms:

15xy - 94x - 69x = 611

Combine like terms again:

15xy - 163x = 611

Now, since L is parallel to M, the slopes of the lines must be equal. The slope of the line represented by the equation is 15x.

The slope of L is unknown, so we can substitute it as a value. Since the slopes are equal, we set them equal to each other:

15x = 15

Divide both sides by 15 to solve for x:

x = 1

Finally, substitute the value of x back into the original equation and solve for y:

(5y - 23) / (2(1) + 13) = 47 / (3(1))

4y - 23 = 47

4y = 70

y = 17.5

Therefore, the values of x and y in the equation are x = 1 and y = 17.5. None of the provided options (a, b, c, d) match these values.