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Chapter 6 | Linear systems
22. The fixed costs (FC) of a factory for the month are $5000 and the variable costs (VC) to manufacture each product
are $5. The total costs (TC) for the month are the sum of the fixed costs and the variable costs per unit, times
the number of products produced and sold. The relationship between TC, FC, VC, and x is given by the equation
TC = (VC)x + FC.
a. What would be the total cost if 90 products were sold this month?
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b. How many products were sold this month if the total cost is $11,375?
6
Answers to odd-numbered problems are available at the end of the textbook
1.
In which quadrant or axis do the following points
8.
lie?
2.
3.
a. A (5, -1)
b. B (-2, 3)
c. C (3, 0)
d. D (4, -2)
e. E (2, 0)
f. F (0, 4)
In which quadrant or axis do the following points
lie?
a. A (-4, 5)
b. B (-5, 0)
c. C (-2, -7)
d. D (0, -3)
e. E (6, 6)
f. F (5, 4)
Plot the following points and join them in the order
A, B, C, D. Identify the type of quadrilateral and
find its area and perimeter.
4.
5.
b. B (6, -6)
c. C (-2, -6)
d. D (-2, -3)
c. x = 2y
9.
Graph the following equations using the slope and
y-intercept method.
a. y = 4x + 6
b. y = - 3 x - 1
4
c. 3x + 2y - 12 = 0
10. Graph the following equations using the slope and
y-intercept method.
Plot the following points and join them in the order
11. Find the equation of the line that passes through
the following points:
a. (3, 2) and (7, 5)
find its area and perimeter.
c. (1, -2) and (4, 7)
a. P (-2, 4)
b. Q (-8, 4)
c. R (-8, -2)
d. S (-2, -2)
Graph the following equations using a table of
values with four points:
b. x + y - 4 = 0
Graph the following equations using a table of
a. 2x + 3y = 12
c. y = - 1 x - 2
3
12. Find the equation of the line that passes through
the following points:
a. (4, 6) and (2, 4)
b. (0, -7) and (-6, -1)
c. (3, -4) and (-1, 4)
13. Solve the following pairs of equations by using the
graphing method:
a. y = -2x - 1 and y = 3x - 11
c. 2y = x and y = -x + 3
14. Solve the following pairs of equations by using the
y-intercept, and another point.
c. y = 4x
b. (5, -4) and (-1, 4)
b. 2x - 3y - 6 = 0 and x + 2y - 10 = 0
b. x + 2y - 4 = 0
Graph the following equations using the x-intercept,
a. 3x - 4y = 12
b. y = - 1 x - 1
3
c. 2x + 3y + 6 = 0
P, Q, R, S. Identify the type of quadrilateral and
values with four points:
7.
y-intercept, and another point.
b. 3x + y - 4 = 0
a. x - 2y = -1
a. y = 5x + 4
a. A (6, -3)
a. 4x - y = 2
c. y = 1 x +2
2
6.
Graph the following equations using the x-intercept,
b. x - 2y - 6 = 0
graphing method:
a. y = 2x + 3 and y = -2x - 1
b. 3x + 4y - 5 = 0 and 2x - y + 4 = 0
c. 3y = 2x and y = -3x + 11
Chapter 6 | Linear Systems
15. Solve the following pairs of equations by using the
substitution method:
18. Solve the following pairs of equations by using the
elimination method:
a. x + 4y = 8 and 2x + 5y = 13
a. 2x + y = 8 and 3x + 2y = 7
b. x + 4y + 12 = 0 and 9x - 2y - 32 = 0
b. 5x - 2y + 3 = 0 and 3x - 2y - 1 = 0
c. 3x + 2y = 5 and y = 2x - 1
c. 2x + y + 2 = 0 and 6x = 2y + 9
16. Solve the following pairs of equations by using the
substitution method:
a. x + y = 3 and 2x - y = 12
b. x - y - 1 = 0 and 2x + 3y - 12 = 0
c. 4x + 3y = 12 and 9 - 3x = y
17. Solve the following pairs of equations by using the
elimination method:
a. 8x + 7y = 23 and 7x + 8y = 22
b. 9x - 2y = -32 and x + 4y = -12
c. 4x + 3y = 12 and 18 - 6x = 2y
19. The slope of a line is 2 and it passes through A (2, 3)
and B (-1, y). Find 'y' and the equation of the line.
20. The slope of a line is -3 and it passes through P (2, -2)
and Q (x, 7). Find 'x' and the equation of the line.
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