Question

It would be greatly be appreciated if someone could try to assist me on this problem

Answer 1

x = -3

y = 5

Explanation:

If polygon ABCDE ≅ KLMNO then:

• AB = KL
• CD = MN

Given:

• 
  `AB = 2y - 3x`
• 
  `CD = 4y + 3x`
• 
  `KL = 6y + 4x + 1`
• 
  `MN = 2y + 1`

Create two equations and rearrange to make 4y the subject:

`\begin{aligned}\implies AB & = KL\\2y - 3x &= 6y + 4x + 1\\2y-3x-2y&=6y+4x+1-2y\\-3x&=4y+4x+1\\-3x-4x&=4y+4x+1-4x\\-7x&=4y+1\\-7x-1&=4y+1-1\\-7x-1&=4y\\4y&=-7x-1\end{aligned}`

`\begin{aligned}\implies CD &= MN\\4y + 3x &= 2y + 1\\4y+3x-2y&=2y+1-2y\\2y+3x&=1\\2y+3x-3x&=-3x+1\\2y&=-3x+1\\2 \cdot 2y&=2 \cdot -3x+2 \cdot 1\\4y&=-6x+2\end{aligned}`

Substitute one equation into the other equation and solve for x:

`\implies -6x+2=-7x-1`

`\implies -6x+2+7x=-7x-1+7x`

`\implies x+2=-1`

`\implies x+2-2=-1-2`

`\implies x=-3`

Substitute the found value of x into one of the equations and solve for y:

`\implies 4y=-6(-3)+2`

`\implies 4y=18+2`

`\implies 4y=20`

`\implies (4y)/(4)=(20)/(4)`

`\implies y=5`