Math week 8
Answer all questions:
Pay attention to the full question (all parts of the question).
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
Show details:
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?
Show details:
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?
Show all work.
Graph your answer.
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?
