Question

PLEASE HELP 100 POINTS

Find the values of x and y in parallelogram PQRS.
PT=​y, TR=2x+​1, QT=4​y, TS=6x+10
x= ? and y= ?

Answer 1

x = 3, y = 7

Explanation:

Diagonals of a parallelogram bisect each other so both halves of each diagonal are equal

PT = TR

QT = TS

y = 2x + 1

4y = 6x + 10

4(2x + 1) = 6x + 10

8x + 4 = 6x + 10

2x = 6

x = 3

y = 2(3) + 1 = 7

Answer 2

x=3 y=7

Explanation:

PT=​y, TR=2x+​1, QT=4​y, TS=6x+10

The diagonals of a parallelogram bisect each other

PT = TR and QT = TS

y = 2x+1 and 4y = 6x+10

We have a system of equations

Multiply the first equation by 4

4y = 8x+4 and 4y = 6x+10

Set them equal

8x+4 = 6x+10

Subtract 6x from each side

8x-6x+4 = 6x-6x +10

2x +4 = 10

Subtract 4

2x+4-4=10-4

2x =6

Divide each side by 2

2x=6/2

x=3

Now solve for y

y = 2x+1

=2(3)+1

=7