Solve the following:
1. Find the slope of the line 3x - y = 5.
2. Find the point of intersection of the lines 2x + y = 4 and 3x - y = 1. Graph the pair of lines.
3. A manufacturer produces items at a daily cost of $1.50 per item and sells them for $2.50 per item. The daily operational overhead is $500. What is the break-even point?
4. Suppose the sales of a company are given by
S(x) = $300x + $3,000 where x is measured in years and x = 0 corresponds to the year 2003.
Find the predicted sales in the year 2006 assuming the trend continues.
5. Write the augmented matrix of the system: x - 2y + z = 3
2x - y = 4
3y + z = 6
6. Perform the row operation R1 + (-2) R2 + R1 on the matrix .
7. y = z x + y = 5.
Determine whether this system has a unique solution, no solution, or infinitely many solutions. If a solution exists, write it down.
8. What are the dimensions of the matrices shown below?
9. a) Find the inverse of: .
b) Use it to solve the following system of equations:
- x1 - x2 - x3 = 1
4 x1 + 5x2 = - 2
x2 - 3 x3 = 3.