Find the values of x and y that make the quadrilateral a parallelogram. Show all your work?

Question

5x-1 3x +9 y+8 Y3-6

Answer 1

I'm assuming those are side lengths, in order (i.e. adjacent sides and not opposite pairs). I'm also assuming that "Y3" means "3y" and isn't a typo.

If that's the case, you'd solve the 1st and 3rd sides being equal in length, and the 2nd and 4th. That's a requirement of a parallelogram -- opposite sides are equal length. (It also works if those are the measures of angles, as opposite angles are also equal.)

5x - 1 = y + 8
and
3x + 9 = 3y - 6

Place the two equations in terms of y:

5x - 1 = y + 8
y = 5x - 9

3x + 9 = 3y - 6
x + 3 = y - 2
y = x + 5

Since both of those equations now equal y, they also equal each other:

5x - 9 = x + 5
4x = 14
x = 3.5

Then use either origination equation with the known value for x to solve for y:

5x - 1 = y + 8
5*3.5 - 1 = y + 8
17.5 - 1 = y + 8
8.5 = y

Just to be safe, use the other to check:

3x + 9 = 3y - 6
x + 3 = y - 2
(3.5 + 3) =? (8.5 - 2)
6.5 = 6.5

The answer is x=3.5 and y=8.5

Answer 2

properly as all of us comprehend the parallel components of a parallelogram are congruent to a minimum of one yet another so this is the form you sparkling up for "y": y + 8 = 3y - 6 y - 3y = -14 -2y = -14 y = 7 You do the comparable concern for "x": 5x - a million = 3x + 9 2x = 10 x = 5