Astudent bought 3 boxes of pencils and 2 boxes of pens for $6. he then bought 2 boxes of pencils and 4 boxes of pens for $8. find the cost of each box of pencils and each box of pens

Let c and n represent the numbers of pencil and pen boxes, respectively
.. 3c +2n = 6.00
.. 2c +4n = 8.00

You can halve the second equation and subtract it from the first to get
.. (3c +2n) -(c +2n) = 6.00 -4.00
.. 2c = 2.00
.. c = 1.00

Then
.. 1.00 +2n = 4.00 . . . . . half the original second equation with c filled n
.. 2n = 3.00
.. n = 1.50

A box of pencils costs $1.00; a box of pens costs $1.50.

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