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Question 1-) Which equation represents an inequality in the system of inequalities shown in the graph?

A-) y > 2x + 2
B-) y > -2x - 1
C-) y < 2x + 2
D-) y < -2x - 1

Question 2-) Which point is a solution to the system?

A-) (-4,-2)
B-) (-1,-2)
C-) (1,4)
D-) (2,2)

Question 1-) Which equation represents an inequality in the system of inequalities-example-1

1 Answer

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The graph of the system inequalities indicates that the inequality in the system and the point which is a solution are;

Question 1) y < 2·x + 2

Question 2) (-1, -2)

What is an inequality; An inequality is an expression that shows the relationship between expressions that have different values or amounts

The points on the graphs are;

Graph of first inequality (0, 2), and (-1, 0)

The slope is; 2/1 = 2

Equation of the first inequality is; y - 2 = 2·(x - 0)

y = 2·x + 2

The shaded region and the type of line in the inequality indicates, the correct inequality symbol is <, therefore; y < 2·x + 2

Graph of second inequality (2, 3), and (0, -1)

The slope is; (3 - (-1))/(2 - 0) = 2

Equation of the second inequality is; y - 3 = 2·(x - 2)

y = 2·x - 4 + 3

y = 2·x - 1

The shaded region and the type of line in the inequality indicates, the correct inequality symbol is ≥, therefore; y ≥ 2·x - 1

The equation that represents an inequality in the system is the option C

C. y < 2·x + 2

Question 2); A solution point is a point that is common to both of the system

The point (-4, -2) is located above the feasible region

The point (-1, -2) is in the feasible region, and therefore, represents a solution of the inequality

The point (1, 4) is in on the dashed line y < 2·x + 2 and therefore, is not in the feasible region

The point (2, 2) is not in the feasible region

The correct option is option B (-1, -2)

User Nuno Tomas
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