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I need help with this please!!

I need help with this please!!-example-1
User FrozenKiwi
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1 Answer

6 votes

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

User LethalMango
by
8.0k points

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