How do I graph the system of inequalities (shade each half-plane solution, not the overall solution) using `y lt= 3/2 x + 3`   and  `2x + y lt 10`   and  `ygt-1` ? Please show all steps and how this looks on a graph.  Thanks!

Expert Answers

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Graph `y<=3/2x+3, 2x+y <10,and y > -1.`

Test point (0,0) y<=3/2x+3

`0lt= 3/2(0) + 3 `

`0 lt= 0+3 `

`0lt=3`

True, graph line and region containing (0,0)

This graph looks like: graph in blue.

Test point (0,0) for 2x+y <10

2(0)+0 < 10

0+0 <10

0<10

True, graph line as...

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Graph `y<=3/2x+3, 2x+y <10,and y > -1.`

Test point (0,0) y<=3/2x+3

`0lt= 3/2(0) + 3 `

`0 lt= 0+3 `

`0lt=3`

True, graph line and region containing (0,0)

This graph looks like: graph in blue.

Test point (0,0) for 2x+y <10

2(0)+0 < 10

0+0 <10

0<10

True, graph line as dashed (not =) and region containing (0,0) 

This graph looks like: graph in red.

y > -1 is horizontal dashed line through -1

This graph looks like:  in green.

Solution to all 3 is triangle created by all 3 intersections.

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