# Lines, matrices, and supply and demand

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1) Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $ 147 for 3 days and 300 miles, while Mary was charged $ 268 for 5 days and 600 miles. What does Best Rental charge per day and per mile?

Write an equation for the line. Use slope-intercept form, if possible.

2) Through ( 5, -6) and ( 0, -8)

Use the echelon method to solve the system of two equations in two unknowns.

3) 5x - 7y = 8

3x - 4y = 5

Write the augmented matrix for the system. Do not solve.

4) -2x + 6y = 40

2x + 2y = 8

Find the slope of the line passing through the given pair of points.

5) ( 3, 2) and ( 3, 9)

Use the echelon method to solve the system of three equations in three unknowns.

6) x + y + z = 2

x - y + 5z = 0

4x + y + z = 14

Find the slope of the line.

7) A line parallel to 4y - 5x = -7

Use the echelon method to solve the system.

8) x/2 + y/2 = 0

x - y = -12

Solve the problem.

9) Let the supply and demand functions for a certain model of electric pencil sharpener be given by

p = S(q) = 2/3q and p = D(q) = 15 - 4/3q

where p is the price in dollars and q is the quantity of pencil sharpeners (in hundreds). Graph these functions on the same axes (graph the supply function as a dashed line and the demand function as a solid line). Also, find the equilibrium quantity and the equilibrium price.

Find the slope of the line.

10) A line parallel to -4x = 5y + 11

Use the echelon method to solve the system of two equations in two unknowns.

11) x - 2y = -2

6x - 3y = -30

Provide an appropriate response.

12) Find k so that the line through (3, k) and (1, -2) is parallel to 5x - 3y= -2. Find k so that the line is perpendicular to 3x + 2y = 6

Write an equation for the line. Use slope-intercept form, if possible.

13) Through ( 4, 0), m = -1

Write the augmented matrix for the system. Do not solve.

14) 4x - 2y = 14

-2y = -2

Find the slope of the line passing through the given pair of points.

15) ( 5, 4) and ( 2, 2)

Use the Gauss-Jordan method to solve the system of equations.

16) 3x + 3y = -6

2x + 8y = 14

Write an equation for the line. Use slope-intercept form, if possible.

17) Through ( 3, 5), m = - 5/9

Find the slope of the line.

18) 5x + 2y = 16

Use the echelon method to solve the system of two equations in two unknowns.

19) x + 3y = 9

-7x + 4y = 12

Find the slope of the line passing through the given pair of points.

20) ( 6, -4) and ( -7, 1)

#### Solution Summary

This works with solving systems of two and three equations, graphing linear equations, and supply and demand function.