Solve each system of linear equations.

$$\begin{array}{r} -2 x+4 y-z=-1 \\ x+7 y+2 z=-4 \\ 3 x-2 y+3 z=-3 \end{array}$$

Rewrite each of the fo llowing linear equations in the form y = mx + b, and give the slope and intercept of the corresponding plot. Then draw the graph. (a) y = 4x - 7, (b) 7x - 2y = 5, (c) 3y + 6x - 4 = 0

Rewrite each of the following equations in $y=a b^{x}$ form. a. $y=16(2)^{2 n-2}$ b. $y=(4)^{\frac{1}{2} x+2}$ c. $y=60\left(\frac{1}{2}\right)^{3 x+1}$ d. $y=81\left(\frac{4}{9}\right)^{\frac{1}{2} x+2}$

Solve the given system of equations below by substitution. Check your answer.

$$\left\{\begin{array}{l}y=-4 x \\ y=2 x-3\end{array}\right.$$

If possible, solve the system.

$$\begin{array}{c} \text{x\hspace{18pt}+ z = 4}\\ \text{\hspace{12pt}$-$y+ z = 2}\\ \text{\hspace{10pt}$-$x+y$-$z = $-$3}\\ \end{array}$$

Graph each system of linear inequalities. Describe the solutions.

$$\left\{ \begin{array} { l } { y \leq - 3 x + 4 } \\ { y \leq - 3 x - 3 } \end{array} \right.$$

Write the following fractions in order of magnitude, starting with the largest:

$$\frac{1}{2} \quad \frac{1}{3} \quad \frac{6}{13} \quad \frac{4}{5} \quad \frac{7}{18} \quad \frac{2}{19}$$

Equations of the form $r^2=a \sin 2 \theta$ and $r^2=a \cos 2 \theta$ describe lemniscates. Graph the lemniscates. $r^2=-8 \cos 2 \theta$

Rewrite the following fractions in simplest form:
(a) $\frac{84}{144}$

(b) $\frac{208}{272}$

(c) $\frac{-930}{1290}$

(d) $\frac{325}{231}$

Find an LU-factorization of the matrix.

$$\left[\begin{array}{rrr} {2} & {0} & {0} \\ {0} & {-3} & {1} \\ {10} & {12} & {3} \end{array}\right]$$

The given equations are in quadratic form. Solve and give the exact solutions.

$$\begin{array}{lrr} 2\text{(ln\hspace{1pt}x)}^\text{2}+9\text{ln\hspace{1pt}x}=5\\ \end{array}$$

For the following exercises, write the equation for the hyperbola in standard form if it is not already, and identify the vertices and foci, and write equations of asymptotes. $-4 x^{2}+40 x+25 y^{2}-100 y+100=0$

Convert each equation to standard form by completing the square on x and y. Then graph the hyperbola. Locate the foci and find the equations of the asymptotes.

$$9 y ^ { 2 } - 4 x ^ { 2 } - 18 y + 24 x - 63 = 0$$

Tell whether the ordered pair is a solution of the system of linear inequalities.

$$(-5, 2) ; \left. \begin{array} { l } { y < 4 } \\ { y > x + 3 } \end{array} \right.$$