"

Systems Of Linear Equations

Prep for Systems of Linear Equations

    1. [latex]x=8[/latex]
    2. one
    3. A number line marked from -4 to 14. A solid (filled) dot is located at x=8.
    1. answers may vary
    2. infinitely many
    3. A Cartesian coordinate plane displays a straight line with a negative slope, descending from the upper left to the lower right. The line crosses the y-axis at the point (0, 5) and the x-axis at the point (5, 0), representing the linear equation.
    1. [latex](2,3)[/latex]
    2. one
    3. A Cartesian coordinate plane with two intersecting straight lines. One line slopes upward from the lower left to the upper right (positive slope), and the other slopes downward from the upper left to the lower right (negative slope). The two lines intersect at the point (2,3).
  1. [latex]\begin{array}{l}\text{B}\hspace{1em}x+y=6\\\text{D}\hspace{1em}3x-4y=1\\\text{C}\hspace{1em}-y=3x-9\\\text{A}\hspace{1em}y=2x-7\end{array}[/latex]
  1. [latex]21x - 14y = 56[/latex]
  2. [latex]6x - y = 27[/latex]
  3. [latex]-4x + 10 = 40[/latex]
  4. [latex]-\frac{6}{7}x = -2y - 16[/latex]
  1. [latex]y = \frac{3}{2}x + 4[/latex]
  2. [latex]y = -x + 3[/latex]
  3. [latex]y = -\frac{2}{3}x + 5[/latex]
  4. [latex]y = x - 3[/latex]
  5. [latex]y = -x + 4[/latex]
  6. [latex]y = -2x - 1[/latex]
  7. [latex]y = \frac{3}{4}x - 6[/latex]
  8. [latex]y = \frac{4}{5}x - 10[/latex]
  9. [latex]y=\frac{-1}4x+3[/latex]
  1. x = the number of fill-in-the-blank questionsy = the number of multiple choice questions
  2. x = the number of grams of medicine Ay = the number of grams of medicine B
  3. x = the cost of a small boxy = the cost of a large box
  4. x = the number of childreny = the number of adults

Systems of Linear Equations

  1. No, the given point does not satisfy the second equation.
    1. [latex](3,6)[/latex]
    2. [latex](-1,3)[/latex]
    3. No solution
    4. [latex]\left(\frac47,\frac{27}7\right)[/latex]
    1. 45 cats and 60 dogs
    2. 203 adults and 226 children
    3. 15 tens and 6 fives
    4. $40,000 at 0.50% and 90,000 at 1.1%

Matrices

  1. [latex]A\;=\;3\times2,\;B\;=\;3\times2,\;C\;=\;2\times3,\;D\;=\;2\times1[/latex]
    1. [latex]\begin{bmatrix}5&-4&9\\1&-2&-3\end{bmatrix}[/latex]
    2. [latex]\begin{bmatrix}3&-2&-3&-5\\1&2&3&-3\\-1&4&-6&-1\end{bmatrix}[/latex]
  3. [latex]\left\{\begin{array}{l}3x-2y+4z=6\\9x+4y-z=0\\6x-8y-3z=3\end{array}\right.[/latex]
  4. [latex]\left(-7,4\right)[/latex]

Homework: Systems of Linear Equations

    1. [latex]4\times2[/latex]
    1. [latex](0, 8)[/latex]
    2. No Solution
    3. [latex](4, 6)[/latex]
    4. [latex](-1, 2)[/latex]
    5. [latex](-1, 8)[/latex]
    6. [latex]\left(-\frac{65}{4}, \frac{35}{16}\right)[/latex]
    7. [latex](-9, 3)[/latex]
    8. [latex]\left(\frac{33}{23}, \frac{96}{23}\right)[/latex]
    1. Sour Sillies: $2.00, Choco Nuts: 1.50
    2. 14 two-pointers and 8 free throws
    3. 12 pigs and 5 chickens
    4. 100 children and 35 adults
    5. tree: $75.00, bush: $25.00
    6. 15 true/false and 5 multiple choice
    7. 30 g of medicine A and 6 grams of medicine B
    8. $13.00

Fractions

    1. Check with a classmate.
    2. Many answers are possible.
    3. Compare with a neighbor.
    1. [latex]\frac{1}{12}[/latex]
    2. [latex]\frac{5}{16}[/latex]
    3. [latex]\frac{7}{9}[/latex]
    4. [latex]\frac{4}{21}[/latex]
    5. [latex]\frac{1}{10}[/latex]
    6. [latex]\frac{52}{81}[/latex]
    7. [latex]\frac{21}{40}[/latex]
    8. [latex]7 \frac{1}{10}[/latex]
    9. [latex]\frac{7}{18}[/latex]
    10. [latex]\frac{8}{9}[/latex]
    1. Reduce to lowest terms.
    2. Find the LCD.
    3. Find the LCD.
    4. Reciprocal mistake.

Applications with Fractions

    1. 8 lbs
    2. 8 teams
    3. [latex]33\frac14\text{lbs}[/latex]
    4. [latex]12\frac58\text{mpg}[/latex]
    5. 5 lbs
    6. [latex]5\frac15\text{laps}[/latex]

Homework: Fractions

    1. [latex]\frac{3}{4}[/latex]
    2. [latex]8 \frac{1}{4}[/latex]
    3. [latex]\frac{8}{9}[/latex]
    4. [latex]5 \frac{8}{15}[/latex]
    5. [latex]\frac{6}{35}[/latex]
    6. [latex]4 \frac{5}{9}[/latex]
    7. [latex]1 \frac{7}{24}[/latex]
    8. [latex]3 \frac{10}{21}[/latex]
    9. [latex]2 \frac{14}{27}[/latex]
    10. [latex]16 \frac{25}{36}[/latex]
    11. [latex]\frac{11}{18}[/latex]
    12. [latex]2 \frac{10}{27}[/latex]
    13. [latex]6 \frac{1}{3}[/latex]
    14. [latex]3 \frac{13}{20}[/latex]
    15. [latex]6 \frac{3}{5}[/latex]
    16. [latex]2 \frac{1}{8}[/latex]
    1. Find the LCD.
    1. [latex]1 \frac{7}{8}[/latex]
    2. [latex]7 \frac{7}{12}[/latex]
    3. [latex]\frac{7}{10}[/latex]
    4. [latex]\frac{1}{6}[/latex]
    5. [latex]\frac{8}{9}[/latex] servings
    6. 6 cupcakes, [latex]\frac{1}{6}[/latex] oz left
    7. [latex]14 \frac{8}{15}[/latex] mi
    8. [latex]1 \frac{1}{2}[/latex] qts
    9. [latex]8 \frac{3}{4}[/latex] bags

Order of Operations

    1. [latex]578[/latex]
    2. [latex]-104[/latex]
    3. [latex]4[/latex]
    4. [latex]13[/latex]
    5. [latex]25 \frac{1}{14}[/latex]
    6. [latex]1 \frac{11}{120}[/latex]
    7. [latex]-108[/latex]
    8. [latex]21[/latex]
    9. [latex]-7[/latex]
    10. [latex]\frac{7}{60}[/latex]
    11. [latex]4[/latex]
    12. [latex]-27[/latex]
    13. [latex]\frac{2}{3}[/latex]
    14. [latex]1 \frac{1}{15}[/latex]
    15. [latex]\frac{9}{2}[/latex]

Solving Linear Equations

    1. [latex]x = 0[/latex]
    2. [latex]x = \frac{4}{3}[/latex]
    3. [latex]x = -\frac{3}{2}[/latex]
    4. All real numbers
    5. [latex]t = 9[/latex]
    6. [latex]x = 1[/latex]
    7. [latex]x = \frac{1}{2}[/latex]
    8. [latex]x = \frac{35}{46}[/latex]
    9. No solution
    10. [latex]x = -16[/latex]
    11. [latex]x = -36[/latex]
    12. [latex]x = \frac{79}{77}[/latex]

Linear Expressions and Equations

    1. [latex]\frac{7}{12}x - 1[/latex]
    2. [latex]x = \frac{12}{7}[/latex]
    3. [latex]\frac{13}{4}x[/latex]
    4. [latex]x = 8[/latex]
    5. [latex]\frac{x-9}{2}[/latex]
    6. [latex]x = 9[/latex]

Homework: Order of Operations and Linear Equations

    1. [latex]1[/latex]
    2. [latex]1[/latex]
    3. [latex]75[/latex]
    4. [latex]\frac{1}{30}[/latex]
    5. [latex]2[/latex]
    6. [latex]15[/latex]
    7. [latex]-15[/latex]
    8. [latex]17[/latex]
    9. [latex]1 \frac{24}{25}[/latex]
    10. [latex]\frac{55}{216}[/latex]
    11. [latex]\frac{6}{7}[/latex]
    12. [latex]\frac{25}{96}[/latex]
    13. [latex]\frac{25}{78}[/latex]
    14. [latex]\frac{7}{12}[/latex]
    15. [latex]1 \frac{409}{1152}[/latex]
    1. [latex]x = 18[/latex]
    2. [latex]x = -3[/latex]
    3. [latex]x = 8[/latex]
    4. [latex]x = \frac{2}{3}[/latex]
    5. [latex]x = -6[/latex]
    6. [latex]x = 18[/latex]
    7. [latex]x = 6[/latex]
    8. [latex]x = -3[/latex]
    9. [latex]c = 12[/latex]
    10. [latex]x = 1[/latex]
    11. [latex]x = \frac{4}{3}[/latex]
    12. [latex]x = 2[/latex]
    13. [latex]x = \frac{5}{3}[/latex]
    14. [latex]x = -\frac{28}{5}[/latex]
    15. [latex]x = -\frac{28}{15}[/latex]
    16. [latex]x = -5[/latex]
    17. [latex]x = \frac{2}{15}[/latex]
    18. [latex]x = 0[/latex]
    19. [latex]x = 11[/latex]
    20. [latex]x = 3[/latex]
    21. [latex]x = 4[/latex]
    22. [latex]x = 6[/latex]
    23. [latex]x = 6[/latex]
    24. [latex]x = -22[/latex]
    25. [latex]x = -6[/latex]
    26. [latex]x = -\frac{5}{19}[/latex]
    27. [latex]x = -\frac{70}{19}[/latex]
    28. No solution

Operations with Polynomials

    1. [latex]6a^3 + 2a[/latex]
    2. [latex]-\frac{12}{5}a^3 + \frac{8}{5}a^2 + 9a[/latex]
    3. [latex]\frac{18}{5}a^3 + \frac{16}{7}a^2 - \frac{5}{7}a[/latex]
    4. [latex]16x^2 - 24x + 9[/latex]
    5. [latex]x^3 - 27[/latex]
    6. [latex]-r^2 - 12r + 25[/latex]

Applications with Polynomials

    1. [latex]5x^2 + 5x + 2[/latex]
    2. [latex]3x^2 - 20x + 25[/latex]
    3. [latex]10x + 10[/latex]
    4. [latex]x^2 + 42x + 360[/latex]

Greatest Common Factor

    1. [latex]6(y^2 + 1)[/latex]
    2. [latex]y^2(x - 3)[/latex]
    3. [latex]3x(x + 2)[/latex]
    4. [latex]4y^2(4x^2 - 7x + 12y^3)[/latex]
    5. [latex]5x^2y^3(5xy - 13y^2 - 16x^2)[/latex]

Homework: Operations with Polynomials, Applications, & GCF

    1. [latex]6x[/latex]
    2. [latex]4[/latex]
    3. [latex]9x^2 - 4[/latex]
    4. [latex]6x + 4[/latex]
    5. [latex]9x^2 + 12x + 4[/latex]
    6. [latex]12x^2 - x - 35[/latex]
    7. [latex]3x^2y + 3xy - 23[/latex]
    8. [latex]7x - 1[/latex]
    9. [latex]x^3 + 12x^2 + 3x + 4[/latex]
    10. [latex]7x - 1[/latex]
    11. [latex]18x^2 + 9x - 35[/latex]
    12. [latex]x^2 + 7x + 10[/latex]
    13. [latex]3x^2 + 2x + 1[/latex]
    14. [latex]x^2 + 6x + 9[/latex]
    15. [latex]3x^2 + 2x + 1[/latex]
    16. [latex]-x^2 - 2x + 10[/latex]
    1. [latex]4x^3 + 4x^2[/latex]
    2. [latex]2x^2 + 10x + 3[/latex]
    1. [latex]3x(2x + 5)[/latex]
    2. [latex]18x^3(2 + 5x^2 - 4x^4)[/latex]
    3. [latex]2x(x - 6)[/latex]
    4. [latex]2(7x^2 - 6x + 4)[/latex]
    5. [latex]2x(7x^2 - 6x + 4)[/latex]
    6. [latex]16x(2x - 1)[/latex]
    7. [latex]8(4x^2 - 2x + 1)[/latex]

 

License

Icon for the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

College Algebra for Non-STEM Majors Copyright © by Northwest Vista College Mathematics Department is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

Share This Book