7. Systems of Equations & Matrices

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x²+y²≤1, y−x²>0

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Graph the solution set of each system of inequalities.

2x + y > 2

x - 3y < 6

Find the value of the objective function z = 2x + 3y at each corner of the graphed region shown. What is the maximum value of the objective function? What is the minimum value of the objective function?

Find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 1. Objective Function z=40x+50y

An objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

Graph the solution set of each system of inequalities.

$y>x^2+2$

$y\(\le\) x-2$

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

$\(\begin{cases}\)x^2 + y^2 \(\leq\) 16 \\(\x\) + y > 2\(\end{cases}\)$

An objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

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

$\(\begin{cases}\)x + y > 4 \\(\x\) + y < -1\(\end{cases}\)$

An objective function and a system of linear inequalities representing constraints are given. a. Graph the system of inequalities representing the constraints. b. Find the value of the objective function at each corner of the graphed region. c. Use the values in part (b) to determine the maximum value of the objective function and the values of x and y for which the maximum occurs.

Match each inequality with the appropriate calculator graph in A–D. Do not use a calculator y ≤ -3x - 6

Graph the solution set of each system of inequalities.

$y\le \log x$

$y\ge \mid x-2\mid$

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.

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is a piecewise function. Refer to the textbook.

Graph the system of inequalities and indicate the region (if any) of solutions satisfying all equations.

$3x-2y>6$

$3x-2y$ < $-4$

Write the given sentences as a system of inequalities in two variables. Then graph the system. The sum of the x-variable and the y-variable is at most 4. The y-variable added to the product of 3 and the x-variable does not exceed 6.