Chapter 9

Write each system in an augmented matrix. $$\begin{array}{r}x-7 y=15 \\\4 x+3 y=-1\end{array}$$

Graph each inequality on a number line and represent the sets of numbers using interval notation. $$-1 \leq p \leq 5$$

Objective 1 In your own words, explain the meaning of the absolute value of a number.

Write each system in an augmented matrix. $$\begin{array}{c}x+6 y=4 \\\\-5 x+y=-3\end{array}$$

The graphs of linear inequalities are given next. For each, find three points that satisfy the inequality and three that are not in the solution set. \(2 x+3 y \leq 18\)

Graph each inequality on a number line and represent the sets of numbers using interval notation. $$7

Does \(|x|=-8\) have a solution? Why or why not?

Write each system in an augmented matrix. $$\begin{aligned}x+6 y-z &=-2 \\\3 x+y+4 z &=7 \\\\-x-2 y+3 z &=8\end{aligned}$$

The graphs of linear inequalities are given next. For each, find three points that satisfy the inequality and three that are not in the solution set. \(y<3 x+4\)

Graph each inequality on a number line and represent the sets of numbers using interval notation. $$y<2 \text { or } y>9$$

Objective 2 Solve. $$|q|=6$$

Write each system in an augmented matrix. $$\begin{aligned} x+2 y-7 z &=3 \\ 3 x-5 y &=-1 \\\\-x+& 2 z=-4 \end{aligned}$$

The graphs of linear inequalities are given next. For each, find three points that satisfy the inequality and three that are not in the solution set. \(y>-\frac{2}{5} x-3\)

Graph each inequality on a number line and represent the sets of numbers using interval notation. $$a \leq-8 \text { or } a \geq \frac{1}{2}$$

Solve. $$|z|=7$$

Write a system of linear equations in \(x\) and \(y\) represented by each augmented matrix. $$\left[\begin{array}{rr|r}3 & 10 & -4 \\\1 & -2 & 5\end{array}\right]$$

The graphs of linear inequalities are given next. For each, find three points that satisfy the inequality and three that are not in the solution set. \(x+y<0\)

Graph each inequality on a number line and represent the sets of numbers using interval notation. $$n \leq-\frac{9}{2} \text { or } n \geq \frac{3}{5}$$

Solve. $$|q-5|=3$$

Write a system of linear equations in \(x\) and \(y\) represented by each augmented matrix. $$\left[\begin{array}{rr|r}1 & -1 & 6 \\\\-4 & 7 & 2\end{array}\right]$$

The graphs of linear inequalities are given next. For each, find three points that satisfy the inequality and three that are not in the solution set. \(y-2 x \geq 0\)

Graph each inequality on a number line and represent the sets of numbers using interval notation. $$-\frac{1}{4} \leq q \leq \frac{11}{4}$$

Solve. $$|a+2|=13$$

Write a system of linear equations in \(x\) and \(y\) represented by each augmented matrix. $$\left[\begin{array}{rr|r}1 & -6 & 8 \\\0 & 1 & -2\end{array}\right]$$

Graph each inequality on a number line and represent the sets of numbers using interval notation. $$4

Solve. $$|4 t-5|=7$$

Write a system of linear equations in \(x\) and \(y\) represented by each augmented matrix. $$\left[\begin{array}{ll|r}1 & 2 & 11 \\\0 & 1 & 3\end{array}\right]$$

Graph using the test point method. \(4 x+y \leq 3\)

Graph each inequality on a number line and represent the sets of numbers using interval notation. $$x<-12 \text { or } x>-9$$

Solve. $$|9 x-8|=10$$

Write a system of linear equations in \(x, y,\) and \(z\) represented by each augmented matrix. $$\left[\begin{array}{rrr|r}1 & -3 & 2 & 7 \\\4 & -1 & 3 & 0 \\\\-2 & 2 & -3 & -9\end{array}\right]$$

Graph using the test point method. \(y

Solve each inequality. Graph the solution set and write the answer in interval notation. $$|m| \leq 7$$

Solve. $$|12 c+5|=1$$

Write a system of linear equations in \(x, y,\) and \(z\) represented by each augmented matrix. $$\left[\begin{array}{rrr|r}1 & 4 & -3 & -5 \\\\-1 & 2 & 5 & 8 \\\6 & -2 & -1 & 3\end{array}\right]$$

Graph using the test point method. \(y>\frac{1}{2} x-1\)

Solve each inequality. Graph the solution set and write the answer in interval notation. $$|c|<1$$

Solve each inequality. Graph the solution set and write the answer in interval notation. $$|3 k|<12$$

Solve. $$|1-8 m|=9$$

Write a system of linear equations in \(x, y,\) and \(z\) represented by each augmented matrix. $$\left[\begin{array}{rrr|r}1 & 4 & -7 & -11 \\\0 & 1 & 3 & -1 \\\0& 0 & 1 & 6\end{array}\right]$$

Graph using the test point method. \(4 x+3 y<15\)

Solve each inequality. Graph the solution set and write the answer in interval notation. $$\left|\frac{5}{4} z\right| \leq 30$$

Solve. $$|4-5 k|=11$$

Solve each system using Gaussian elimination. $$\begin{aligned}x+4 y &=-1 \\\3 x+5 y &=4\end{aligned}$$

Graph using the test point method. \(y

Solve each inequality. Graph the solution set and write the answer in interval notation. $$|w-2|<4$$

Solve. $$\left|\frac{2}{3} b+3\right|=13$$

Solve each system using Gaussian elimination. $$\begin{array}{r}x-3 y=1 \\\\-3 x+7 y=3\end{array}$$

Graph using the test point method. \(y \geq 3 x\)

Solve each inequality. Graph the solution set and write the answer in interval notation. $$|k-6| \leq 2$$