Answer
Peaches cost 1.29 per pound, pears cost .69 dollars per pound, and cherries cost .99 dollars per pound.
Work Step by Step
Let g be the cost per pound of peaches, o be the cost per pound of pears, and c be the cost per pound of cherries. Thus:
$ 2g + c + 3o = 5.64 \\ g + 2c + 2o = 4.65 \\ 2g + 4c + o = 7.23$
In order to solve systems of three linear equations, we multiply the first and second equation by values that will cancel out a variable when they are added. Thus, we multiply the first equation by -2 and the second equation by 1 and add to obtain:
$-3g -4o = -6.63$
We now multiply the first and third equation by values that will cancel out a variable when they are added. Thus, we multiply the first equation by -4 and the third equation by one and add to obtain:
$ -6g - 11o = -15.33$
Plugging $-3g = -6.63 + 4o$ into this equation, we obtain:
$-3o -13.26 = -15.33 \\ o = .69 $
Now, we plug this value into one of the equations that only has o and g in them to find:
$ g = 1.29$
Finally, we plug the values of g and o into the first equation listed to find:
$ c = .99$
