Project #5698 - System of Equations/Special Topics

1. Solve the system

{x+3y+2z=7}
{    5y+4z=14}
{            z=1}

 

2. Solve the system

{7x+7y+z=1}
{x+8y+8z=8}
{9x+y+9z=9}

 

3. The matrix associated with the solution to a system of linear equations in x,y,& z is given. Write the solution to the system, if it exists.

[1   -1   3 l -10]
[4   0    1 l  -4 ]
[1   3   1  l -10]

 

4. The matrix associated with the solution to a system of linear equations in x,y,& z is given. Write the solution to the system, if it exists.

[1   0   2  l 2]
[0   1   -3 l 4]
[0   0   0  l 0]

 

5. The matrix associated with the solution to a system of linear equations in x,y,& z is given. Write the solution to the system, if it exists.

[1   0   4 l 2]
[0   1   1 l 4]
[0   0   0 l 0]

 

6. Solve the problem.

Linda invest $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The total income from the 5% and 6% investments is equal to the income from the 8% investment. Find the amount invested at each rate.

 

7. Solve the system.

{x^2+y^2=145}
{x-y=1}

 

8. Write the inequalities that describe the constraints on production.

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. The company can produce up to 24 rings each day, using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to makeone SST ring. Let x represent the number of VIP rings, and let y represent the number of SST rings.
A) 0≤x≤24, 0≤y≤24, 2x+37≤60
B) 0≤x≤24, 0≤u≤24, 3x+2y≤60
C) x+y≤24, 2x+3y≤60, x≥0, y≥0
D) x+y≤24, 3x+2y≤60, x≥0, y≥0

Subject Mathematics
Due By (Pacific Time) 5/8/13
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