Diana purchases 6 pounds of strawberries and 4 pounds of apples for 18.90. then she realized that this was not enough and purchased 3 more pounds of each fruit for 10.74. what was the cost per pound for each type of fruit?

6 pounds of strawberries for x pounds and 4 pounds of apples for y pounds. = $18.90.
6x + 4y = 18.90
Then, you add 3 more pounds of each fruit which equals $10.17. 
3x + 3y = 10.17
Then you multiply by -2 which is (-6x) - 6y = -20.34. After that, you add that (read carefully) you would do this. (-6x) + 6x - 6y + 4y = -20.34 + 28.90.
-2y = -1.44 divided by -2.
Y = -1.44/-2
Y = $0.72 per pound of apples.Now, plus in the value of Y in equation 2.
3x + 3y = 10.17
3x + 3 * 0.72 = 10.17.
3x + 2.16 = 10.17
-2.16
3x = 10.17 - 2.16
3x = 8.06 /3

Int total, X = $2.68 per pound of strawberry. Hope this helps just read it carefully.