# Math week 8

Pay attention to the full question (all parts of the question).

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1.  For the following system of equation, find a solution or show that no solution exists:

2y +3x – 3z  = 16

2x + 3y + 4z = -8

3z + 2x – 5y = 26

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The solution is:  x = 6;   y = -4;  z = -2

2. A goldsmith combined an alloy that costs \$4.30 per ounce with an alloy that costs \$1.80 per ounce. How many ounces of each were used to make a mixture of 200 ounces costing \$2.50 per ounce?

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3. An airplane travels 1,200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air and what is the wind speed?

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4) Write the augmented matrix for the system of equations shown.

5z + 4x + 4y = 22

3x + 7y = -2z -17

4x + 3y + 3z =6

5) Write the system of equations for the augmented matrix shown.

-2   3  4  |  18

-3   4  2  |  5

-2   3  3  |  12

6) For the following system of equation, find a solution or show that no solutionexists:

5y +3z – 4x  = -3z + 3

4z + 6y + 5x = -19

5y + 3x + 4z = -12

7) For the following system of equation, find a solution or show that no solutionexists:

x + y + z  = 1

2x – 3y + 7z = 0

3x – 2y + 8z = 4

8) If 105 people attended a concert and tickets for adults costs \$2.50 while tickets for children cost \$1.75 and total receipts for the concert were \$228, how many children and how many adults went to the concert?