An office supply store recently sold a black printer ink cartridge for $14.99 and a color printer ink cartridge for $23.99. At the start of a recent fall semester, a total of 64 of these cartridges was sold for a total of $1157.36. How many of each type were purchased?

Let B be the number of Black printer ink cartridges and C be the number of color printer ink cartridges.

49 were sold in total, hence,

B+C= 49 (1)

Also, its given that

18.99 B + 27.99 C = 1146.51(2)
Multiplying (1) by 18.99,

18.99 B+ 18.99 C= 930.51 (3)

Now, subtracting (3) from (2),

18.99 B + 27.99 C = 1146.51
18.99 B+ 18.99 C= 930.51

9 C = 216
C= 24

We know, B+ C= 49
Hence B = 49-24 = 25

Hence, number of Black printer ink cartridges = 25 and color printer ink cartridges = 24.

2x+7y=14
=> 7y=14-2x
=> y=14/7-2x/7
=> y=-(2/7)x+2
-(2/7) is the slope