Question

Use the drawing tool(s) to form the correct answer on the provided graph.

Graph the solution to the following system of inequalities in the coordinate plane.

Answer 1

The graph of system of inequalities is shown below.

Explanation:

The given system of inequalities is

`y>(1)/(4)x+6` .... (1)

`y>2x-1` ... (2)

The slope intercept form of a line is

`y=mx+b`

where, m is slope and b is y-intercept.

The related equation of first inequality is

`y=(1)/(4)x+6`

The slope of this line is 1/4 and y-intercept is 6.

The related equation of second inequality is

`y=2x-1`

The slope of this line is 2 and y-intercept is -1.

The sign of inequalities is >, it means the related line is a dotted line and shaded region lies above the line.

Common shaded region represents the solution set.

Answer 2

see below. The solution is the doubly-shaded area.

Explanation:

Each boundary line will be dashed, because the "or equal to" case is not included. Each shaded area will be above the corresponding boundary line because the comparison symbol is y > .... That is, only y-values greater than (above) those in the boundary line are part of the solution.

Of course, the boundary lines are graphed in the usual way. Each crosses the y-axis at the value of the constant in its equation. Each has a slope (rise/run) that is the value of the x-coefficient in the equation.