Question

solve the systems of linear inequalities by graphing. graph the inequalities on your recording sheet. determine whether the ordered pair is a solution. \

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

Explanation:

Step1: Test (-1, 3) in both inequalities

First inequality: $3 < 3(-1) - 2
ightarrow 3 < -5$ (False)
Second inequality: $3 > -(-1) + 3
ightarrow 3 > 4$ (False)

Step2: Test (0, 0) in both inequalities

First inequality: $0 < 3(0) - 2
ightarrow 0 < -2$ (False)
Second inequality: $0 > -(0) + 3
ightarrow 0 > 3$ (False)

Step3: Test (4, 4) in both inequalities

First inequality: $4 < 3(4) - 2
ightarrow 4 < 10$ (True)
Second inequality: $4 > -(4) + 3
ightarrow 4 > -1$ (True)

Step4: Test (2, 1) in both inequalities

First inequality: $1 < 3(2) - 2
ightarrow 1 < 4$ (True)
Second inequality: $1 > -(2) + 3
ightarrow 1 > 1$ (False)

Step5: Test (7, 5) in both inequalities

First inequality: $5 < 3(7) - 2
ightarrow 5 < 19$ (True)
Second inequality: $5 > -(7) + 3
ightarrow 5 > -4$ (True)

Step6: Test (2, 2) in both inequalities

First inequality: $2 < 3(2) - 2
ightarrow 2 < 4$ (True)
Second inequality: $2 > -(2) + 3
ightarrow 2 > 1$ (True)

Step7: Test (4, -6) in both inequalities

First inequality: $-6 < 3(4) - 2
ightarrow -6 < 10$ (True)
Second inequality: $-6 > -(4) + 3
ightarrow -6 > -1$ (False)

Step8: Test (10, -3) in both inequalities

First inequality: $-3 < 3(10) - 2
ightarrow -3 < 28$ (True)
Second inequality: $-3 > -(10) + 3
ightarrow -3 > -7$ (True)

Answer:

SOLUTIONS:

(4, 4), (7, 5), (2, 2), (10, -3)

NOT SOLUTIONS:

(-1, 3), (0, 0), (2, 1), (4, -6)