Question

Parallelogram pqrs has diagonals PR and SQ that intersect at T find the value of X and Y

Answer 1

If a parallelogram PQRS has diagonals PR and SQ that intersects at T, then, T is the midpoint of PR and T is the midpoint of SQ

Given

`\begin{gathered} PT=y \\ TR=3x+1 \end{gathered}`
`y=3x+1`

Also

`\begin{gathered} QT=3y \\ TS=4x+13 \end{gathered}`
`3y=4x+13`

Now we are going to solve the system of equations with two unknowns

`\begin{gathered} y=3x+1 \\ 3y=4x+13 \end{gathered}`

Substitute equation 1 into 2

`\begin{gathered} 3(3x+1)=4x+13 \\ 9x+3=4x+13 \\ 9x-4x=13-3 \\ 5x=10 \\ x=(10)/(5) \\ x=2 \\ \end{gathered}`

x = 2

Substitute x = 2 into equation 1

`\begin{gathered} y=3x+1 \\ y=3(2)+1 \\ y=6+1 \\ y=7 \end{gathered}`

y = 7

The answer would be x = 2, y = 7