If castel bought 6 rose bushes and 1 shrub for $36 and chelsea bought 6 rose bushes and 8 shrubs for $78 how much is the cost of one rose bush and the cost of one shrub

Let us assume the cost of one rose bush = x
let us assume the cost of one shrub = y
Then
Castle bought 6 rose bushes and 1 shrub for $36. The equation can be written as
6x + y = 36
Chelsea bought 6 rose bushes and 8 shrubs for $78. Then the equation can be written as
6x + 8y = 78
Now let us take the first equation first
6x + y = 36
y = 36 - 6x
Now we have to put the value of y in the second equation.
6x + 8y = 78
6x + 8(36 - 6x) = 78
6x + 288 - 48x = 78
-42x = 78 - 288
- 42x = - 210
42x = 210
x = 210/42
   = 5 dollars
Now putting the value of x in the first equation we get
6x + y = 36
6(5) + y = 36
30 + y = 36
y = 36 - 30
   = 6 dollars
So the cost of 1 rose bush is $5 and the cost of a shrub is $6.