Question

Solve the following systems of inequalities and select the correct graph: 2x − y > 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.

Answer 1

The solution to the system of inequalities is given as Graph II.

What is a system of inequalities?

A group of two or more inequalities in one or more variables is referred to as a system of inequalities.

When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are utilized.

What is the calculation leading to the above solution?

The system of inequality,

2x - y < 4

x + y < -1

First we draw the graph of both line. So make table of each line

For line 2x - y < 4

x  :    -1        0        1

y  :    -6     -4       -2

Test point (0,0)

0 - 0 < 4

0 < 4

True (Shade towards origin)

For line x + y < -1

x  :    -1        0        1

y  :    0        -1       -2

Test point (0,0)

0 + 0 < -1

    0 < -1

False (Shade away from origin)

Plot the points graph.

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Full Question:

The graphs associated with the question are attached.