Question

1. ( a x = 2 x ; x b = y + 12 ; d x = 3 y - 8 ; x c = x + 9 ) ( 22. x = ) ( y = ) 23 ( y = )

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So \(AX = XC\) and \(DX = XB\).
For \(AX = XC\), we have the equation \(2x=x + 9\).
Subtract \(x\) from both sides: \(2x-x=x + 9-x\), which gives \(x = 9\).

Step2: Use the other diagonal - bisecting property

Since \(DX = XB\), substitute \(x = 9\) into the equations. We know \(XB=y + 12\) and \(DX=3y-8\).
Set \(y + 12=3y-8\).
Subtract \(y\) from both sides: \(y + 12-y=3y-8-y\), getting \(12 = 2y-8\).
Add \(8\) to both sides: \(12 + 8=2y-8 + 8\), so \(20 = 2y\).
Divide both sides by \(2\): \(y=\frac{20}{2}=10\).

Answer:

\(x = 9\), \(y = 10\)