if AE=3x-6, DE=6y-12, EC=2x+2 and EB=2y+24 find the values of y

Answer 1

We know that AE = DE + EC + EB.

Substituting the given values, we have:

3x - 6 = (6y - 12) + (2x + 2) + (2y + 24)

Simplifying the equation, we get:

3x - 6 = 6y - 12 + 2x + 2 + 2y + 24

Rearranging the terms, we have:

3x - 6 = 6y + 2y - 12 + 2x + 2 + 24

Combining like terms, we get:

3x - 6 = 8y + 2x + 14

Rearranging the terms again, we have:

3x - 2x = 8y - 6 - 14 + 6

Simplifying further, we get:

x = 8y - 14

To solve for y, we can substitute this value of x back into one of the other equations. Let's use AE = 3x - 6.

AE = 3x - 6
3x - 6 = 3(8y - 14) - 6
3x - 6 = 24y - 42 - 6
3x - 6 = 24y - 48

Rearranging the terms, we have:

3x - 24y = -42

Let's solve this equation for x:

3x - 24y = -42
3x = 24y - 42
x = (24y - 42)/3
x = 8y - 14

Since we found earlier that x = 8y - 14, we can conclude that y can be any real number.