5.13.6: Chapter Review
- Page ID
- 129570
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Chapter Review
Algebraic Expressions
Linear Equations in One Variable with Applications
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Linear Inequalities in One Variable with Applications
Ratio and Proportions
Graphing Linear Equations and Inequalities
- Is the ordered pair a solution to the equation?
- Is the point on the line in the graph shown?
/**/{\text{A: }}(0, - 3)\quad \quad {\text{B: }}( - 3,1);\quad \quad {\text{C: }}( - 2, - 4);\quad \quad {\text{D: }}(0,2)/**/
![A line is plotted on a coordinate plane. The horizontal and vertical axes range from negative 10 to 9, in increments of 1. The line passes through the points, (negative 6, 0), (0, 2), and (6, 4).](https://math.libretexts.org/@api/deki/files/110537/CS_Figure_05_CR_005.png?revision=1)
/**/{\text{A: }}(0,0)\quad \quad {\text{B: }}(2,1)\quad \quad {\text{C: }}( - 1, - 5)\quad \quad {\text{D: }}( - 6, - 3)\quad \quad {\text{E: }}(1,0)/**/
![A line is plotted on a coordinate plane. The horizontal and vertical axes range from negative 10 to 9, in increments of 1. The line passes through the points, (negative 1, negative 10), (0, negative 5), (1, 2), and (2, 9). The region to the right of the line is shaded. Note: all values are approximate.](https://math.libretexts.org/@api/deki/files/110539/CS_Figure_05_CR_007.png?revision=1)
Quadratic Equations with Two Variables with Applications
Functions
![Mapping of two sets of values. Mapping infers the following data: 0, negative 2; 1, 1; negative 2, 4, and 3.](https://math.libretexts.org/@api/deki/files/110536/CS_Figure_05_CR_010.png?revision=1)
![Two functions are graphed on a coordinate plane. The horizontal axis ranges from negative 14 to 5, in increments of 1. The vertical axis ranges from negative 9 to 10, in increments of 1. The first function passes through the points, (negative 13, 7.5), (negative 10, 4.5), (negative 6, 0), (negative 10, negative 4.5), and (negative 13, negative 7.5). The second function passes through the points, (4, 9.5), (0, 5.5), (negative 5, 0), (0, negative 5.5), and (4, negative 9.5). Note: all values are approximate.](https://math.libretexts.org/@api/deki/files/110540/CS_Figure_05_CR_011.png?revision=1)
/**/\{ ( - 3,{\rm{ }}9),{\rm{ }}( - 2,{\rm{ }}4),{\rm{ }}( - 1,{\rm{ }}1),{\rm{ }}(0,{\rm{ }}0),{\rm{ }}(1,{\rm{ }}1),{\rm{ }}(2,{\rm{ }}4),{\rm{ }}(3,{\rm{ }}9)\}/**/
![Eight points are plotted on a coordinate plane. The horizontal and vertical axes range from negative 10 to 10, in increments of 1. The points are plotted at the following coordinates: (negative 5, 0), (negative 4, 1), (negative 3, 2), (negative 2, 3), (negative 1, 4), (0, 5), (1, 6), and (2, 7).](https://math.libretexts.org/@api/deki/files/110538/CS_Figure_05_CR_012.png?revision=1)
Graphing Functions
![A line is plotted on a coordinate plane. The horizontal and vertical axes range from negative 10 to 10, in increments of 1. The line passes through the points, (0, negative 8), (4, 0), and (8, 8).](https://math.libretexts.org/@api/deki/files/110543/CS_Figure_05_CR_013.png?revision=1)
![A line is plotted on a coordinate plane. The horizontal and vertical axes range from negative 10 to 10, in increments of 1. The line passes through the points, (negative 8, negative 7), (0, negative 3), (6, 0), and (8, 1).](https://math.libretexts.org/@api/deki/files/110544/CS_Figure_05_CR_015.png?revision=1)
System of Linear Equations in Two Variables
/**/\left\{ {\begin{array}{*{20}{l}}{x - 2y = 0}\\{3x - y = 5}\end{array}} \right./**/
/**/\left\{ {\begin{array}{*{20}{l}}{y = 3x + 1}\\{6x - y = 2}\end{array}} \right./**/
/**/\left\{ {\begin{array}{*{20}{l}}{y = 7x + 2}\\{3x - y = - 6}\end{array}} \right./**/
/**/\left\{ {\begin{array}{*{20}{l}}{ - 5x + y = - 15}\\{3x + y = 17}\end{array}} \right./**/
Systems of Linear Inequalities in Two Variables
5\\ 2x - y \le 10 \end{array} \right." class=" math-rendered">/**/\left\{ \begin{array}{l} 3x + y > 5\\ 2x - y \le 10 \end{array} \right./**/
![Two dashed lines are plotted on a coordinate plane. The horizontal and vertical axes range from negative 10 to 10, in increments of 1. The first line passes through the points, (negative 6, 9), (0, 3), (3, 0), and (8, negative 5). The second line passes through the points, (negative 10, negative 8), (0, negative 1.5), (2.5, 0), and (9, 4.4). The two lines intersect at (2.8, 0.4). The region within the lines and to the left of the intersection point is shaded in gray. The region within the lines and to the right of the intersection point is shaded in dark blue. The region within the lines and below the intersection point is shaded in light blue. Note: all values are approximate.](https://math.libretexts.org/@api/deki/files/110545/CS_Figure_05_CR_019.png?revision=1)
/**/\left\{ {\begin{array}{*{20}{l}}{y < 3x + 1}\\{6x - y \ge 2}\end{array}} \right./**/