MATH 166 Spring 2016
4.4
c
Wen
Liu
4.4 Systems of Linear Equations With Non-Unique Solutions
Examples: Solve the following system of equations. (Enter your answers as a comma-separated list.
If there are infinitely many solutions, enter a parametric solution using t and/or s. If there is no
solution, enter NONE.)
1.

 2x + 2y + 2z = 24
4x + 4y + 4z = 41

3x + 4y + 4z = 41
2.

 3y + 2z = 1
2x − y − 3z = 4

2x + 2y − z = 5
3.

 30x + 5y = 45
2x − 2y = −4

32x + 3y = 41
4. The matrix below is in row-reduced form. Write the corresponding linear system and solve the
system.
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MATH 166 Spring 2016
4.4
c
Wen
Liu
5. A woodworking shop makes foot-stools, coffee tables, and rocking chairs. Each spends time in
a fabrication shop, a gluing shop, and a painting shop. The following table shows the number
of hours each item spends in each shop. If there are 45 hours available in the fabrication shop,
36 hours available in the gluing shop and 81 hours available in the painting shop, how many
of each item can be made if all the available hours are to be used? (Order your answers from
smallest number of rocking chairs to largest number of rocking chairs.)
Foot-stools Coffee tables
Rocking chairs
Scenario #1
Scenario #2
Scenario #3
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