SOLUTION: At the school store, 3 pens and 2 notebooks cost a total of $12, while 1 pen and 3 notebooks cost a total of $11. This can be represented by the system of equations, where x stands

Question 1052319: At the school store, 3 pens and 2 notebooks cost a total of $12, while 1 pen and 3 notebooks cost a total of $11. This can be represented by the system of equations, where x stands for the cost, in dollars, of pens, and y stands for the cost, in dollars, of notebooks.
What is the cost of one notebook?
$2.00
$2.40
$2.75
$3.00
Found 2 solutions by LinnW, addingup:
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
3x + 2y = $12
1x + 3y = $11
Add -3y to the second equation
x = 11 - 3y
Substitute ( 11 - 3y ) for x in 3x + 2y = 12
3 ( 11 - 3y ) + 2y = 12
33 - 9y + 2y = 12
33 - 7y = 12
Add -33 to each side
-7y = -21
Divide each side by -7
y = 3
substitute 3 for y in x = 11 - 3y
x = 11 - 3(3)
x = 11 -9
x = 2
One notebook is $3.00

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
3x+2y = 12 (1)
1x+3y = 11; 1x is the same as just x, so
x+3y = 11 (2)
Multiply both sides of (1) times 3 and both sides of (2) times 2:
9x+6y = 36 (3)
2x+6y = 22 (4)
Now subtract (4) from (3):
9x+6y = 36
-
2x+6y = 22
------------
7x+0y = 14
and here 0y means we don't have any y because 6y-6y=0, so we re-write:
7x = 14 divide both sides by 7
x = 2 This is the cost of a pen
and
x+3y = 11
2+3y = 11
3y = 9
y = 3 This is the cost of a notebook
----------------------
Check:
3x+2y = 12; 3(2)+2(3) = 12; 6+6 = 12 Correct
x+3y = 11; 2+3(3) = 11; 2+9 = 11 Correct
:
John

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