91Ó°ÊÓ

In Exercises \(29-42,\) solve each system by the method of your choice. $$ \left\\{\begin{array}{l} x^{2}+(y-2)^{2}=4 \\ x^{2}-2 y=0 \end{array}\right. $$

write the partial fraction decomposition of each rational expression. $$ \frac{x^{3}+x^{2}+2}{\left(x^{2}+2\right)^{2}} $$

A certain brand of razor blades comes in packages of \(6,12\) and 24 blades, costing 2 dollar , 3 dollar, and 4 dollar per package, respectively. A store sold 12 packages containing a total of 162 razor blades and took in 35 dollar. How many packages of each type were sold?

In Exercises \(29-42,\) solve each system by the method of your choice. $$ \left\\{\begin{array}{l} x^{2}-y^{2}-4 x+6 y-4=0 \\ x^{2}+y^{2}-4 x-6 y+12=0 \end{array}\right. $$

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. $$ \left\\{\begin{array}{l} 4 x-2 y=2 \\ 2 x-y=1 \end{array}\right. $$

write the partial fraction decomposition of each rational expression. $$ \frac{x^{2}+2 x+3}{\left(x^{2}+4\right)^{2}} $$

Solve the system: $$\begin{aligned} w-x+2 y-2 z &=-1 \\ x-\frac{1}{3} y+z &=\frac{8}{3} \\ y-z &=1 \\ z &=3 \end{aligned}$$ Express the solution set in the form \(\\{(w, x, y, z)\\} .\) What makes it fairly easy to find the solution?

Graph the solution set of each system of inequalities or indicate that the system has no solution. $$-2

Consider the following array of numbers:$$\left[\begin{array}{ccc}1 & 2 & -1 \\\ 4 & -3 &-15\end{array}\right]$$ Rewrite the array as follows: Multiply each number in the top row by \(-4\) and add this product to the corresponding number in the bottom row. Do not change the numbers in the top row.

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. $$ \left\\{\begin{array}{l} \frac{x}{4}-\frac{y}{4}=-1 \\ x+4 y=-9 \end{array}\right. $$