Question

Find the values of x and y that make FGHI is a parallelogram

Answer 1

By definition, a parallelogram is a quadrilateral with opposite sides parallel and equal.

Since the opposite sides are equal, the following equations are true

`\begin{gathered} 5x=3x+18 \\ 3y-7=2y+4 \end{gathered}`

Solving the first equation, we have

`\begin{gathered} 5x=3x+18_{} \\ 5x-3x=18 \\ 2x=18 \\ x=(18)/(2) \\ x=9 \end{gathered}`

Solving the second equation, we have

`\begin{gathered} 3y-7=2y+4 \\ 3y=2y+4+7 \\ 3y-2y=11 \\ y=11 \end{gathered}`

And those are the solutions.

`\begin{cases}x=9 \\ y=11\end{cases}`