7. Systems of Equations & Matrices

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 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 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 or indicate that the system has no solution.

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

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

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

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 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≤1, y−x²>0

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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

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 or indicate that the system has no solution.

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

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.

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.

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.