# HW #5 - Yeah, math, whatever. ```HW #5 MAT 110
Name______________________________
Part I Due Tuesday, April 20
(1) Solve the system of linear equations:
 x  4 y  2 z  15

2 x  y  3z  2
3x  2 y  z  3

(2) Find the solutions of the non-linear system:
 y  x2  4x  2

 y   x  12
(3) Decompose into the sum of partial fractions:
x
2
x  3 x  10
(4) Graph the solution set of the system of linear inequalities:
 x  2 y  8,

3x  y  6
(5) Graph the solution set of the non-linear inequality:
( x  3)2  ( y  4)2  9
(6) Find the maximum value of the function P  6 x  8 y subject to the constraints:
2 x  y  12,

 x  3 y  21,
 x  0, y  0

Part II Due Thursday, April 22
(1) Solve the system of linear equations:
 x  6 y  4 z  6,

4 x  3 y  4 z  1,
5 x  9 y  8 z  13

(2) Find the equation of the form y  ax 2  bx  c whose graph passes through the points
(2,3), (-2,7) and (1,-2). (tip plug these points into the equation, then solve the resulting
system for a, b, and c.
(3) Find the solutions of the non-linear system using elimination:
2
2
 x  y  5
 2
2
3 x  2 y  19
(4) Decompose into the sum of partial fractions:
2x 1
x2  4
(5) Graph the solution set of the system of inequalities:
y  x2  2x 1
(6) A farmer has 10 acres to plant in wheat and rye. He has to plant at least 7 acres.
However, he has only \$1200 to spend and each acre of wheat costs \$200 to plant and
each acre of rye costs \$100 to plant. Moreover, the farmer has to get the planting done in
12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye.
If the profit is \$500 per acre of wheat and \$300 per acre of rye how many acres of each
should be planted to maximize profits?
```