Answer:
x = 2 and y = 5
Explanation:
One of the properties of a parallelogram is that the diagonals bisect each other
In the parallelogram PQRS, PR bisects QS at T and QS bisects PR at T
Therefore,
PT = TR and QT = TS
From PT = TS using the given expressions in x, y we get
y = 2x + 1 ............ (1)
From QT = TS using the given expressions in x, y we get
5y = 6x + 13 ............ (2)
We have a set of two equations in x and y which we can use to solve for x and y
Multiply (1) by 5
==> 5y = 5(2x) + 5(1)
==> 5y = 10x + 5 ............ (3)
Equations (2) and (3) both have 5y on the left side. So their right sides must be equal to each other:
10x + 5 = 6x + 13
Subtract 6x from both sides
10x - 6x + 5 = 6x - 6x + 13
4x + 5 = 13
Subtract 5 from both sides:
4x + 5 - 5 = 13 - 5
4x = 8
x = 8/4 = 2
In equation (1) substitute x = 2
y = 2(2) + 1 = 5
Therefore x = 2 and y = 5