Question

the figure below is a quadrilateral. find the values of x and y.
3y - 7
5x
3x + 18
2y + 4
x=
y=

Explanation:

Step1: Identify the quadrilateral type

The quadrilateral has two pairs of equal - length sides (it looks like a parallelogram, where opposite sides are equal). So, we can set up equations for the equal sides. For the sides with \(x\): \(5x=3x + 18\). For the sides with \(y\): \(3y-7 = 2y + 4\).

Step2: Solve for \(x\)

Start with the equation \(5x=3x + 18\). Subtract \(3x\) from both sides: \(5x-3x=3x + 18-3x\), which simplifies to \(2x = 18\). Then divide both sides by 2: \(x=\frac{18}{2}=9\).

Step3: Solve for \(y\)

Take the equation \(3y-7 = 2y + 4\). Subtract \(2y\) from both sides: \(3y-2y-7=2y + 4-2y\), which gives \(y - 7=4\). Then add 7 to both sides: \(y=4 + 7 = 11\).

Answer:

\(x = 9\), \(y=11\)