Answer:
x = 4.5 and y = 3
Explanation:
Area of a rectangle = length x width
= 12 (2x - y)
Area is given as 72
∴ 12 (2x - y ) = 72
Divide both sides by 12 =>
12/12 (2x - y) = 72/12
2x - y = 6 [1]
The kite perimeter is 33
Your equation is correct:
2(3x) + 2(y) = 33
=> 6x + 2y = 33 [12]
So we have two equations and we can solve them as follows
Multiply [1] by 2
2(2x -y) = 2 x 6
4x - 2y = 12 [3]
Coefficients of y in equations [1] and [2] are same but of opposite sign
Add [1] and [3]
6x + 2y = 33
+
4x - 2y = 12
-------------------------
10x + 0 = 45
=> 10x = 45
Divide both sides by 10
=> x= 45/10
x = 4.5
Substitute for x in equation [1]: 2x - y = 6
=> 2(4.5) - y = 6
=> 9 - y = 6
Subtract 9 from both sides
9 - 9 - y = 6 - 9
-y = -3
Multiply by -1 both sides
y = 3
Answer: x = 4.5 and y = 3