91Ó°ÊÓ

The first step in solving a system of equations by the method of _____ is to obtain coefficients for \(x\) (or y ) that differ only in sign.

A solution of a system of three linear equations in three unknowns can be written as an _____, which has the form \(( x , y , z )\)

Graphically, the solution of a system of two equations is the_______________of__________________of the graphs of the two equations.

You obtain the _______ ______ after multiplying each side of the partial fraction decomposition form by the least common denominator.

Solving a Linear Programming Problem, find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. (For each exercise, the graph of the region determined by the constraints is provided.) $$ \begin{array}{c}{\text { Objective function: }} \\ {z=2 x+5 y} \\ {\text { Constraints: }} \\ {x \geq 0} \\ {y \geq 0} \\ {x+3 y \leq 15} \\ {4 x+y \leq 16}\end{array} $$

Solving a Linear Programming Problem, find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. (For each exercise, the graph of the region determined by the constraints is provided.) $$ \begin{array}{l}{\text { Objective function: }} \\ {z=10 x+7 y} \\ {\text { Constraints: }} \\ {0 \leq x \leq 60} \\ {0 \leq y \leq 45} \\ {5 x+6 y \leq 420}\end{array} $$

Solving a Linear Programming Problem, sketch the region determined by the constraints. Then find the minimum and maximum values of the objective function (if possible) and where they occur, subject to the indicated constraints. $$ \begin{array}{c}{\text { Objective function: }} \\ {z=3 x+2 y} \\ {\text { Constraints: }} \\ {x \geq 0} \\ {5 x+2 y \leq 20} \\ {5 x+y \geq 10}\end{array} $$

Using Back-Substitution In Exercises \(11 - 16 ,\) use back-substitution to solve the system of linear equations. $$\left\\{ \begin{aligned} 4 x - 2 y + z & = 8 \\ - y + z & = 4 \\ z & = 11 \end{aligned} \right.$$

Finding Minimum and Maximum Values, find the minimum and maximum values of the objective function and where they occur, subject to the constraints \(x \geq 0, y \geq 0,3 x+y \leq 15\) and \(4 x+3 y \leq 30 .\) $$ z=x+y $$

In Exercises 19-28, use a graphing utility to graph the inequality. $$2 x^{2}-y-3>0$$