Question

Help with all of this

1. The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the system, if a solution exists. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answers in terms of z as in Example 3.)

2x − 5y + z = 8

x + 4y − 6z = 4

3x − 4y − 2z = 12

(x, y, z) =

2. The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the system, if a solution exists. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answers in terms of z as in Example 3.)

3x − 2y + 5z = 10

2x − 3y + 4z = 7

(x, y, z) =

3. A preschool has Campbell's Chunky Beef soup, which contains 2.5 g of fat and 15 mg of cholesterol per serving (cup), and Campbell's Chunky Sirloin Burger soup, which contains 7 g of fat and 15 mg of cholesterol per serving. By combining the soups, it is possible to get 28 servings of soup that will have 142 g of fat and 420 mg of cholesterol. How many cups of each soup should be used?

beef cups

burger Cups

4. A man has $270,000 invested in three properties. One earns 12%, one 10% and one 8%. His annual income from the properties is $25,800 and the amount invested at 8% is twice that invested at 12%.

(a) How much is invested in each property?

12% property $

10% property $

8% property $

(b) What is the annual income from each property?

12% property $

10% property $

8% property $

Answer 1

Solutions for q1 and q2

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