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

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

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