Linear inequality system solutions Practice Questions

Warm-upeasy

$\begin{cases} y > 3x - 5 \\ y \le x + 4 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $x = 2$ , which of the following could be a value of $y$ ?

Substitute $x = 2$ . From $y > 3x - 5$ , $y > 1$ . From $y \le x + 4$ , $y \le 6$ . The value $y = 4$ satisfies $1 < 4 \le 6$ .

Mid-gameeasy

$\begin{cases} y \ge -x + 3 \\ y < 2x + 7 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $x = 1$ , which of the following could be a value of $y$ ?

Substitute $x = 1$ . From $y \ge -x + 3$ , $y \ge 2$ . From $y < 2x + 7$ , $y < 9$ . The value $y = 5$ satisfies $2 \le 5 < 9$ .

Mid-gameeasy

$\begin{cases} y \le -x + 10 \\ y > x - 1 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $x = 4$ , which of the following could be a value of $y$ ?

Substitute $x = 4$ . From $y \le -x + 10$ , $y \le 6$ . From $y > x - 1$ , $y > 3$ . The value $y = 5$ satisfies $3 < 5 \le 6$ .

Mid-gameeasy

$\begin{cases} y \ge 2x + 1 \\ y \le x + 5 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $x = 0$ , which of the following could be a value of $y$ ?

Substitute $x = 0$ . From $y \ge 2x + 1$ , $y \ge 1$ . From $y \le x + 5$ , $y \le 5$ . The value $y = 3$ satisfies $1 \le 3 \le 5$ .

Mid-gamemedium

$\begin{cases} x + y \le 10 \\ x \ge y - 2 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $y = 6$ , which of the following could be a value of $x$ ?

Substitute $y = 6$ . From $x + y \le 10$ , $x \le 4$ . From $x \ge y - 2$ , $x \ge 4$ . The only listed value that satisfies both is $x = 4$ .

Mid-gamemedium

$\begin{cases} 2x - y \ge 4 \\ x + y \le 7 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $y = 2$ , which of the following could be a value of $x$ ?

Substitute $y = 2$ . From $2x - y \ge 4$ , $2x - 2 \ge 4$ , so $x \ge 3$ . From $x + y \le 7$ , $x \le 5$ . The value $x = 4$ satisfies $3 \le 4 \le 5$ .

Mid-gamemedium

$\begin{cases} x - 2y < -3 \\ x + y > 6 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $y = 5$ , which of the following could be a value of $x$ ?

Substitute $y = 5$ . From $x - 2y < -3$ , $x - 10 < -3$ , so $x < 7$ . From $x + y > 6$ , $x + 5 > 6$ , so $x > 1$ . The value $x = 4$ satisfies $1 < 4 < 7$ .

Buzzer beatermedium

$\begin{cases} y \ge 2x + 1 \\ y \le x + 9 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $y = 8$ , which of the following could be a value of $x$ ?

Substitute $y = 8$ . From $y \ge 2x + 1$ , $8 \ge 2x + 1$ , so $x \le \dfrac{7}{2}$ . From $y \le x + 9$ , $8 \le x + 9$ , so $x \ge -1$ . The value $x = 2$ satisfies both inequalities.

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