7. Systems of Equations & Matrices

Graph each inequality. y < x² - 1

Graph the solution set of each system of inequalities.

$y\(\le\) x^3-x$

$y>-3$

Graph each inequality. 2x > 3 - 4y

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

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

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

$x+y\(\le\)4$

$y\(\ge\)1$

$x>0$

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 each inequality. y > (x - 1)² + 2

In Exercises 39–45, graph each inequality. y ≤ (-1/2)x + 2

In Exercises 63–64, write each sentence as an inequality in two variables. Then graph the inequality. The y-variable is at least 4 more than the product of -2 and the x-variable.

Graph the solution set of each system of inequalities or indicate that the system has no solution. −2≤x<5

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

$\(\begin{cases}\)x \(\geq\) 0 \\(\y\) \(\geq\) 0 \\2x + 5y < 10 \\3x + 4y \(\leq\) 12\(\end{cases}\)$

Graph the solution set of each system of inequalities.

$x\le 4$

$x\ge 0$

$y\ge 0$

$x+2y\ge 2$

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

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

Graph the solution set of each system of inequalities.

4x - 3y ≤ 12

y ≤ x²

Graph the solution set of each system of inequalities.

$3x-2y\ge 6$

$x+y\le -5$

$y\le 4$