Question

If ON= 5x - 7, LM = 4x+ 4, NM = x -7, and OL =3y-4, find the values of c and y for which LMNO MUST BE a parallelogram.

Answer 1

x=11, y=8/3

Explanation:

Consider quadrilateral LMNO. If this quadrilateral MUST BE a parallelogram, then

LM=NO

and

LO=MN

Thus,

`\left\{\begin{array}{l}4x+4=5x-7\\ \\x-7=3y-4\end{array}\right.`

Solve this system of two equations. From the first equation:

`4x-5x=-7-4\\ \\-x=-11\\ \\x=11`

Substitute it into the second equation:

`11-7=3y-4\\ \\3y-4=4\\ \\3y=4+4\\ \\3y=8\\ \\y=(8)/(3)`