(16/y)+(24/x)=4; (24/y)+(18/x)=4.5 find x and y values?

1/y = a
1/x = b

16a + 24b = 4
24a + 18b = 4.5

16a + 24b = 4
4a + 6b = 1
4a = 1 - 6b
24a = 6 - 36b

6 - 36b + 18b = 4.5
6 - 18b = 4.5
12 - 36b = 9
3 = 36b
1/12 = b

4a = 1 - 6b
4a = 1 - 1/2
4a = 1/2
a = 1/8

1/y = 1/8
1/x = 1/12

(16/y) + (24/x) = 4 …… [1]
(24/y) + (18/x) = 4.5 …… [2]

Let b = 1/y and a = 1/x, the two equations become :
16b + 24a = 4 …… [3]
24b + 18a = 4.5 …… [4]

[1] * (3/2) :
24b + 36a = 6 …… [5]

[5] - [4] :
18a = 1.5
18/x = 1.5
x = 18/1.5
x = 12

Substitute x = 12 into [1] :
(16/y) + (24/12) = 4
16/y = 2
y = 16/2
y = 8

Hence, (x, y) = (12, 8)

Let a=1/x
Let b=1/y

24a+16b=4 ----(1)
18a+24b= 4.5 ----(2)

multiply equation (1) by -24 and equation (2) by 16
-576a -384b = -96
288a + 383b = 72

add:
-288a = -24

a = 4/288
a=1/12

24a+16b = 4 -----(1)
24(1/12) + 16b = 4
2 + 16b = 4
16b = 2
b = 2/16 = 1/8

a=1/12
1/x = 1/12
x = 12

b= 1/8
1/y = 1/8
y= 8

x=12; y=8

Divide the first equation by 4 and the second by 3, and note 4.5 = 9/2:
4/y + 6/x = 1
8/y + 6/x = 3/2
subtract top equation from bottom equation
8/y - 4/y = 1/2
(8-4)/y = 1/2
4/y = 1/2, so
y=8
plug that into 4/y + 6/x = 1 and get
1/2 + 6/x = 1, so
6/x=1/2, so
x=12
summary:
x=12, y=8