91Ó°ÊÓ

Solving a System by Elimination In Exercises \(13-30,\) solve the system by the method of elimination and check any solutions algebraically. $$ \left\\{\begin{array}{l}{3 x+2 y=10} \\ {2 x+5 y=3}\end{array}\right. $$

Solving a System by Substitution In Exercises \(15-24\) , solve the system by the method of substitution. $$\left\\{\begin{array}{l}{2 x-y+2=0} \\ {4 x+y-5=0}\end{array}\right.$$

Solving a Linear Programming Problem, use a graphing utility to graph the region determined by the constraints. Then find the minimum and maximum values of the objective function and where they occur, subject to the constraints. $$ \begin{array}{c}{\text { Objective function: }} \\ {z=3 x+y} \\ {\text { Constraints: }} \\ {x \geq 0} \\ {y \geq 0} \\ {x+4 y \leq 60} \\ {3 x+2 y \geq 48}\end{array} $$

In Exercises 5-18, sketch the graph of the inequality. $$y \leq \frac{1}{1+x^{2}}$$

Solving a System by Elimination In Exercises \(13-30,\) solve the system by the method of elimination and check any solutions algebraically. $$ \left\\{\begin{array}{r}{2 r+4 s=5} \\ {16 r+50 s=55}\end{array}\right. $$

In Exercises 5-18, sketch the graph of the inequality. $$y>\frac{-15}{x^{2}+x+4}$$

Solving a System by Substitution In Exercises \(15-24\) , solve the system by the method of substitution. $$\left\\{\begin{array}{c}{6 x-3 y-4=0} \\ {x+2 y-4=0}\end{array}\right.$$

Writing the Partial Fraction Decomposition. Write the partial fraction decomposition of the rational expression. Check your result algebraically. $$\frac{3}{x^{2}-3 x}$$

Performing Row Operations In Exercises 17 and \(18 ,\) perform the row operation and write the equivalent system. Add \(- 2\) times Equation 1 to Equation 3 $$\left\\{ \begin{aligned} x - 2 y + 3 z = 5 & \text { Equation } 1 \\ - x + 3 y - 5 z = 4 & \text { Equation } 2 \\\ 2 x - 3 z = 0 & \text { Equation } 3 \end{aligned} \right.$$ What did this operation accomplish?

Solving a Linear Programming Problem, use a graphing utility to graph the region determined by the constraints. Then find the minimum and maximum values of the objective function and where they occur, subject to the constraints. $$ \begin{array}{c}{\text { Objective function: }} \\ {z=x} \\ {\text { Constraints: }} \\ {x \geq 0} \\ {y \geq 0}\end{array} $$ $$ \begin{array}{l}{2 x+3 y \leq 60} \\ {2 x+y \leq 28} \\ {4 x+y \leq 48}\end{array} $$