Question 1127524
Let burgers be x, fries y, and drink z
solving by elimination:
x + y + z = 5.50 = 11/2 multiply all times 2 to get rid of the fraction
x + 0 + z = 4.00 = 4
x + y + 0 = 4.25 = 17/4 multiply all times 4 to get rid of the fraction
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2x + 2y + 2z = 11
x + 0y + z = 4
4x + 4y + 0z = 17
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Swap rows 1 and 2:
x + 0y + z = 4
2x + 2y + 2z = 11
4x + 4y + 0z = 17
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Multiply the first equation times -2 and add to the 2nd equation:
-2x + -0y + -2z = -8
+2x + 2y + 2z = 11
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0x + 2y + 0z = 3
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now we have:
x + z = 4
2y = 3
4x + 4y = 17
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multiply the firs equation times -4 and add to the 3rd equation:
-4x + 0y -4z = -16
+ 
4x + 4y + 0z = 17
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0x + 4y + -4z = 1
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now we have:
x + z = 4
2y = 3
4y - 4z = 1
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swap rows 2 and 3:
x + z = 4
4y - 4z = 1
2y = 3; y = 3/2
Now that we know the value of y, let's find z:
4y - 4z = 1
4(3/2) - 4z = 1
6-4z = 1 
-4z = -5
z = 5/4
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Now in the first equation solve for x by substituting y= 3/2 and z = 5/4. You can do this yourself, you should get 11/4 so that:
burger = 11/4 = $2.75
fries = 3/2 = $1.50
drink = 5/4 = $1.25
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P.s. you can also solve this problem with a system of matrices using Cramer's Rule but you didn't say.
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Happy learning!