# graph the system of inequalites and graph (shade each half plane solution not only the overall solution). y<_3/2x+3,2x+y<10,y>-1.

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### 1 Answer

Graph the system of inequalities:

`y<=3/2x+3`

`2x+y<10`

`y > -1`

Graph the three underlying lines:

(`y=3/2x+3` is the solid line, 2x+y=10 is the slanted dotted line, while y=-1 is the horizontal dotted line. The dotted lines are dotted sincee the inequality is strict; i.e. points on the lines are not solutions to the inequality.

The grapher does not allow me to show shading; ideally you would choose three colors (or patterns) to shade with.

Use red to color the inequality `y<=3/2x+3` , blue 2x+y<10, and green to color y>-1.

Then for the solid line the half-plane that includes the origin is shaded red. For 2x+y<10 the half-plane that includes the origin is colored blue. And the half-plane above y=-1 is colored green. The triangle will be colored all three colors.