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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
[tex]\begin{gathered} PT=y \\ TR=3x+1 \end{gathered}[/tex][tex]y=3x+1[/tex]Also
[tex]\begin{gathered} QT=3y \\ TS=4x+13 \end{gathered}[/tex][tex]3y=4x+13[/tex]Now we are going to solve the system of equations with two unknowns
[tex]\begin{gathered} y=3x+1 \\ 3y=4x+13 \end{gathered}[/tex]Substitute equation 1 into 2
[tex]\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}[/tex]x = 2
Substitute x = 2 into equation 1
[tex]\begin{gathered} y=3x+1 \\ y=3(2)+1 \\ y=6+1 \\ y=7 \end{gathered}[/tex]y = 7
The answer would be x = 2, y = 7
