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.