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

To solve the given systems of inequalities by graphing, begin by rearranging each inequality to isolate y, remembering to reverse the inequality sign when dividing or multiplying both sides by a negative number:

Inequality 1:

[tex]2x-y < 4\\\\-y < -2x+4\\\\y > 2x-4[/tex]

Inequality 2:

[tex]x+y > -1\\\\y > -x-1[/tex]

Now, graph each inequality on the coordinate plane and identify the region where the shaded areas of both inequalities overlap. This overlapping region represents the solution to the system of inequalities.

For y > 2x - 4, graph the boundary line y = 2x - 4, but as the inequality sign is ">", use a dashed line to represent it. Shade above the line. This inequality is represented in yellow on the attached graph and labelled A.

For y > -x - 1, graph the boundary line y = -x - 1, but as the inequality sign is ">", use a dashed line to represent it. Shade above the line. This inequality is represented in blue on the attached graph and labelled B.

The area where they have shading in common is the green overlapping region labeled AB. This area represents the solution to the system of inequalities.