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

Question

Answer 1

For this to be a parallelogram the sides opposite each other must be the same length. So:

4x + y = 42 and

3x - 2y = 26

Using the elimination method of solving simultaneous linear equations, multiply the first equation by 2 and add it to the second equation.

2 x (eqn. 1) = 8x + 2y = 84

1 x (eqn. 2) = 3x - 2y = 26

and adding them gives:

11x = 110

x = 10

Find y by using eqn. 1:

4(10) + y = 42

y = 42 - 40

y = 2

Answer 2

Opposite sides of a parallelogram are congruent therefore to be a parallelogram

4x+y=42 and 3x-2y=26

This problem has been solved by Joseph S using the elimination method hence I will use the substitution method to solve it. I would only use substitution if one of the equations is easily solved for either x or y.

In the first equation, 4x+y=42, you can subtract 4x from both sides you can solve for y.

y=-4x+42

The next step would be to replace/substitute -4x+42 in the second equation (3x-2y=26) for y.

3x-2(-4x+42)=26

Distribute the -2

3x+8x-84=26

Combine like terms

11x-84=26

Add 84 to both sides then divide both sides by 11

11x=110

x=10

Remember you must then find y by substituting 10 for x. You can substitute into either of the equations but using y=-4x+42 is the easiest

y=-4(10)+42

y=-40+42

y=2

x=10 and y=2 is the final answer