7. Systems of Equations & Matrices

In Exercises 57–59, graph the region determined by the constraints. Then find the maximum value of the given objective function, subject to the constraints. This is a piecewise function. Refer to the textbook.

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

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

Graph the inequality $y$ < $2^{x}$.

In Exercises 39–45, graph each inequality. 3x - 4y > 12

Graph each inequality. x≤−3

Graph the solution set of each system of inequalities.

y ≥ (x - 2)² + 3

y ≤ -(x - 1)² + 6

Graph each inequality. y≥x²−9

Graph each inequality. y>2^x

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

$\(\begin{cases}\)y > 2x - 3 \\(\y\) < -x + 6\(\end{cases}\)$

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

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

Graph each inequality. x² + (y + 3)² ≤ 16

Graph the solution set of each system of inequalities.

x + y ≥ 0

2x - y ≥ 3

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\(\end{cases}\)$

Graph the solution set of each system of inequalities.

$y\(\ge\)3^{x}$

$y\(\ge\)2$