Question

Which ordered pairs are in the solution set of the system of linear inequalities?
y > -1/2x

y < 1/2x + 1

A (5, –2), (3, 1), (–4, 2)
B (5, –2), (3, –1), (4, –3)
C (5, –2), (3, 1), (4, 2)
D (5, –2), (–3, 1), (4, 2)

Answer 1

The solution set of C works for both equations. 

You can find this by looking for true statements when you put each of the ordered pairs into each of the equations. 

Ordered Pair #1 (5, -2)
y > -1/2x 
-2> -1/2(5)
-2> -2.5 (TRUE)

y < 1/2x + 1
-2 < 1/2(5) + 1
-2 < 2.5 + 1
-2 < 3.5 (TRUE)

Ordered Pair #2: (3, 1)
y > -1/2x 
1 > -1/2(3)
1> -1.5 (TRUE)

y < 1/2x + 1
1 < 1/2(3) + 1
1 < 1.5 + 1
1 < 2.5 (TRUE)

Ordered Pair #3: (4,2)
y > -1/2x 
2 > -1/2(4) 
2 > -2 (TRUE)

y < 1/2x + 1
2 < 1/2(4) + 1
2 < 2 + 1
2 < 3 (TRUE)

Answer 2

The order pairs  (5, –2), (3, 1), (4, 2) lie on in the solution region of the inequalities , Option C is the answer.

What is an Inequality ?

Inequality is a mathematical statement formed when two algebraic expressions are equated by Inequality Operator .

The system of Inequalities given are

y > -1/2x

y < 1/2x + 1

The order pairs that are is solution set can be determined by plotting a graph and then substituting the values in the graph , if the points lie in the solution region.

It can be seen from the graph that the order pairs  (5, –2), (3, 1), (4, 2) lie on in the solution region of the inequalities , which is represented by red dots in the graph.

Therefore Option C is the answer.

To know more about Inequality

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