7. Systems of Equations & Matrices

In Exercises 65–68, 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 no more than 2. The y-variabe is no less than the difference between the square of the x-variable and 4.

Graph each inequality. y>2x−1

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

$\(\begin{cases}\)(x - 1)^2 + (y + 1)^2 < 25 \\(x - 1)^2 + (y + 1)^2 \(\geq\) 16\(\end{cases}\)$

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. x²+y²<16, y≥2^x

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

$\(\begin{cases}\)2x - 5y \(\leq\) 10 \\3x - 2y > 6\(\end{cases}\)$

Graph the solution set of each system of inequalities. x + 2y ≤ 4 y ≥ x² - 1

Graph each inequality. y > 2^x + 1

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

$\(\begin{cases}\)3x + 6y \(\leq\) 6 \\2x + y \(\leq\) 8\(\end{cases}\)$

In Exercises 27–62, graph the solution set of each system of inequalities or indicate that the system has no solution. 3x+y≤6, 2x−y≤−1, x>−2, y<4

Graph the solution set of each system of inequalities.

3x + 5y ≤ 15

x² + y² < 9

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=5x+6y

The graphs show regions of feasible solutions. Find the maximum and minimum values of each objective function. objective function = 3x + 5y

Graph each inequality. y>−3

Graph each inequality. (x−2)²+(y+1)²<9

Graph each inequality. x + 2y ≤ 6