Question

1. in parallelogram defg, dh = x + 2, hf = 2y, gh = 3x - 3, and he = 5y + 1. find the values of x and y.

x = 11, y = 20

x = 18, y = 10

x = 20, y = 11

x = 10, y = 18

Explanation:

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. So, $DH = HF$ and $GH=HE$.
We get the equations: $x + 2=2y$ and $3x - 3=5y + 1$.

Step2: Rearrange the first - equation

From $x + 2=2y$, we can express $x$ in terms of $y$ as $x=2y - 2$.

Step3: Substitute $x$ into the second - equation

Substitute $x = 2y-2$ into $3x - 3=5y + 1$.
$3(2y - 2)-3=5y + 1$.
Expand the left - hand side: $6y-6 - 3=5y + 1$.
Simplify to get $6y-9 = 5y + 1$.

Step4: Solve for $y$

Subtract $5y$ from both sides: $6y-5y-9=5y-5y + 1$.
$y-9 = 1$.
Add 9 to both sides: $y=10$.

Step5: Solve for $x$

Substitute $y = 10$ into $x=2y - 2$.
$x=2\times10 - 2=18$.

Answer:

$x = 18,y = 10$