Question

The following is a parallelogram. Find x and y using the given information.
AB=5x-2y
DC=4
AD=y
BC=5-x

Answer 1

diagram ?

Answer 2

use the lengths of the opposite sides are equal for parallelogram

Answer 3

or i guess x is 2 and y is 3

Answer 4

for guessing i have assumed 5x-2y=4 or AB=DC
and 5-x=y or AD=BC

Answer 5

AB = DC
5x - 2y = 4

AD = BC
y = 5 - x

substitute second equation into the first
5x - 2(5 - x) = 4

simplify
5x - 10 + 2x = 4

combine like terms
7x - 10 = 4

add 10 to both sides
7x -10 + 10 = 4 + 10

simplify
7x + 0 = 14
7x = 14

divide by 7
7x/7 = 14/7

simplify
1x/1 = 2
x = 2

back substitute into either of the original two equations to get y.
5(2) - 2y = 4
10 - 2y = 4
10 - 4 = 2y
6 = 2y
3 = y

conclude that x = 2 and y = 3.