Exercise 53 Page 520

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

In a parallelogram opposite sides are congruent. Therefore DC and AB are congruent, and BC and AD are congruent too. This means that each pair of sides has the same length. Let's compare the lengths and write a system of equations. 5x+y= 13 & (I) 13x-3y= 17 & (II) Let's solve this system. We will start by isolating y in Equation (I).

5x+y= 13 & (I) 13x-3y= 17 & (II)

SubEqn

(I):LHS-5x=RHS-5x

y=13-5x 13x-3y=17

We have isolated the y-variable. We will continue by substituting y in Equation (II).

y=13-5x 13x-3y=17

Substitute

(II):y= 13-5x

y=13-5x 13x-3( 13-5x)=17

▼

(II): Solve for x

Distr

(II):Distribute - 3

y=13-5x 13x-39+15x=17

AddTerms

(II):Add terms

y=13-5x 28x-39=17

AddEqn

(II):LHS+39=RHS+39

y=13-5x 28x=56

DivEqn

(II):.LHS /28.=.RHS /28.

y=13-5x x=2

Now that we found that x=2, let's substitute it in Equation (I).

y=13-5x x=2

Substitute

(I):x= 2

y=13-5( 2) x=2

Multiply

(I):Multiply

y=13-10 x=2

SubTerm

(I):Subtract term

y=3 x=2

We found that x=2 and y=3, which corresponds to choice H.