Question

the solution set to the following system of inequalities is graphed in the coordinate plane below
2x - y > 1
4x + y > 3
what is wrong with the graph?
a one line is graphed incorrectly because the wrong slope is used.
b one line is graphed incorrectly because the wrong y-intercept is used.
c the boundary lines create four regions and the shaded region does not represent the solution to the system
d nothing is wrong with the graph, the graph correctly represents the solution to the system

Explanation:

Step1: Analyze the first inequality \(2x - y > 1\)

Rewrite it in slope - intercept form (\(y=mx + b\)): \(y<2x - 1\). The slope \(m = 2\) and \(y\) - intercept \(b=- 1\).

Step2: Analyze the second inequality \(4x + y>3\)

Rewrite it in slope - intercept form: \(y>-4x + 3\). The slope \(m=-4\) and \(y\) - intercept \(b = 3\).

Step3: Check the boundary lines and shaded region

The boundary lines' slopes and intercepts seem to be graphed correctly. But the solution to a system of inequalities is the region that satisfies both inequalities. The shaded region in the graph does not represent the intersection (solution) of the two half - planes defined by \(2x - y>1\) and \(4x + y>3\). The boundary lines create four regions, and the shaded region is not the one that satisfies both inequalities. So the error is that the boundary lines create four regions and the shaded region does not represent the solution to the system.

Answer:

C. The boundary lines create four regions and the shaded region does not represent the solution to the system