Question

practice analyzing solutions to a system of two - variable linear inequalities.
which ordered pairs make both inequalities true?
check all that apply.
(-2, 2)
(0, 0)
(1, 1)
(1, 3)
(2, 2)
the inequalities are (ygeq-\frac{1}{5}x + 1) and (ylt2x + 1) (with a graph showing the regions for these inequalities).

Explanation:

Step1: Identify the inequalities

The system is:
$y \geq -\frac{1}{5}x + 1$
$y < 2x + 1$

Step2: Test (-2, 2)

Substitute into first inequality: $2 \geq -\frac{1}{5}(-2) + 1 = \frac{2}{5}+1=1.4$ (true)
Substitute into second inequality: $2 < 2(-2)+1=-4+1=-3$ (false)

Step3: Test (0, 0)

Substitute into first inequality: $0 \geq -\frac{1}{5}(0)+1=1$ (false)
Substitute into second inequality: $0 < 2(0)+1=1$ (true)

Step4: Test (1, 1)

Substitute into first inequality: $1 \geq -\frac{1}{5}(1)+1=-\frac{1}{5}+1=0.8$ (true)
Substitute into second inequality: $1 < 2(1)+1=3$ (true)

Step5: Test (1, 3)

Substitute into first inequality: $3 \geq -\frac{1}{5}(1)+1=0.8$ (true)
Substitute into second inequality: $3 < 2(1)+1=3$ (false, not less than)

Step6: Test (2, 2)

Substitute into first inequality: $2 \geq -\frac{1}{5}(2)+1=-\frac{2}{5}+1=0.6$ (true)
Substitute into second inequality: $2 < 2(2)+1=5$ (true)

Answer:

(1,1), (2, 2)