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 chart has a coordinate plane with the inequality (ygeq-\frac{1}{5}x + 1) (a blue line) and (ylt2x + 1) (a dashed orange line), and different shaded regions.

Explanation:

Step1: Define the two inequalities

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

Step2: Test (-2, 2)

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

Step3: Test (0, 0)

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

Step4: Test (1, 1)

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

Step5: Test (1, 3)

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

Step6: Test (2, 2)

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

Answer:

(1,1), (2,2)