Exercise 23 Page 501

Let's find the values of both variables at one time.

Values of x and y

Notice that the sides with lengths 6y+ 12x and 2x+4y are opposite to each other. Moreover, the sides with lengths 21 and 3x+3y are also opposite to each other. Let's recall the Parallelogram Opposite Sides Theorem.

Therefore, if we want the given quadrilateral to be a parallelogram, the opposite sides must be congruent. 6y+ 12x=2x+4y & (I) 21=3x+3y & (II) We will solve the system by using the Substitution Method. Let's start by isolating the x-variable in Equation (II).

Now that x is isolated in Equation (II), we will substitute x=7-y in Equation (I), and solve for y.

We found that y=3. Finally, we will find the value of x by substituting this value in Equation (II).