8 cakes and 3 pies cost a total of 6.40. 5 cakes and 2 pies cost a total of 4.05. work out the cost of a cake?

Let x be the cost of a cake, and y be the cost of a pie.

8x + 3y = 6.40 …… [1]
5x + 2y = 4.05 …… [2]

[1] * 2 :
16x + 6y = 12.80 …… [3]

[2] * 3 :
15x + 6y = 12.15 …… [4]

[3] - [4] :
(16x - 15x) + (6y - 6y) = 0.65
x = 0.65

The cost of a cake = 0.65

8 c + 3 p = 640
5 c + 2 p = 405

-16 c - 6 p = - 1280
15c + 6p = 1215________add

- c = - 65
c = 65

520 + 3p = 640
3p = 120
p = 40

Cake cost is 65
Pie cost is 40

What is unit of currency ?

On my calculator,
.. rref([[8, 3, 6.40] [5, 2, 4.05]])
= [[1 0 .65]
.. [0 1 .4]]

A cake cost 0.65.

_____
You can also use Cramer's rule:
.. cake cost = (3*4.05 -2*6.40)/(3*5 -2*8) = -0.65/-1 = 0.65

8c+3p = 6.40
16c + 6p = 12.80

5c+2p = 4.05
-15c - 6p = -12.15

 16c + 6p = 12.80
-15c - 6p = -12.15
----------------------
  c    = 0.65

cake is $0.65

Let the cost of a cake be $x
Let the cost of a pie be $y
8x+3y=6.40 ----(1)
5x+2y=4.05 ----(2)


Multiply equation (1) by -2 and equation (2) by 3
-16x-6y =-12.80
15x+6y =12.15
add:

-x = -0.65
x= $0.65 (cost of a cake)

Thank you