Question

What values must x and y have to make the quadrilateral a parallelogram?

Short answer

The values that x and y must have to make the quadrilateral a parallelogram are 10 and 2 respectively.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Description of step.

In a parallelogram, both pairs of opposite sides are congruent.

Therefore, to make the given quadrilateral a parallelogram, the pairs of opposite sides are congruent.

Therefore, it can be obtained as:

$\begin{array}{c}4x+y=42\left(1\right)\\ 3x-2y=26\left(2\right)\end{array}$

From the equation, it can be obtained as:

$\begin{array}{c}4x+y=42\\ y=42-4x\end{array}$

Step 3. Find the value of x.

Now, substitute the value of y in equation (2) to find the value of x.

Therefore, the value of x can be obtained as:

$\begin{array}{c}3x-2\left(42-4x\right)=26\\ 3x-84+8x=26\\ 11x-84=26\\ 11x=26+84\\ 11x=110\\ x=\frac{110}{11}\\ x=10\end{array}$

Therefore, the value of x is 10.

Step 4. Find the value of y.

Now, substitute 10 for x in the equation $y=42-4x$to find the value of y.

Therefore, the value of y can be obtained as:

$\begin{array}{c}y=42-4\left(10\right)\\ =42-40\\ =2\end{array}$

Therefore, the value of y is 2.