If 5 apples and 4 oranges cost $ 3.40 while 7 apples and 6 oranges cost $ 4.90, find the cost of an apple and an orange.

We'll establish the cost of an apple as x and the cost of an
orange as y.

We'll write mathematically the phrase "5 apples and 4
oranges cost $ 3.40":

5x + 4y = 3.4
(1)

We'll write mathematically the phrase " 7 apples and 6 oranges
cost $ 4.90":

7x + 6y = 4.9 (2)

We'll
solve the system using elimination method. We'll add 6*eq.(1) +
(-4)*eq.(2):

30x + 24y - 28x - 24y = 20.4 -
19.6

We'll combine and eliminate like
terms:

2x = 0.8

x =
0.8/2

x = $ 0.4

We'll substitute x in
eq.(1):

5*0.4 + 4y = 3.4

2 + 4y =
3.4

4y = 3.4 - 2

4y =
1.4

y = 1.4/4

y =
0.7/2

y = $ 0.35

So, the cost of an
apple is $ 0.4 and the cost of an orange is $ 0.35.