Question

Which is the graph of the system x+3y>-3 and y <1/2x+1?

Answer 1

First you'll need to isolate the equations so that y is on one side.

y is already on the left side in the second equation, so let's do the same for the first equation.

x+3y > -3

1. Subtract x from both sides.

3y > -3-x

2. Divide both sides by 3.

y > -1-1/3x

Now you have two equations that you can graph.

1. y > -1-1/3x
2. y < 1/2x + 1

I'll try to explain how to graph them, but I'll also attach a graph.

y > -1-1/3x

• Go to -1 on the y axis and go down 1, over 3 units. The line will be a dotted line because > is not equal to as well. Since it is greater than, >, you will shade above the line you make.

y < 1/2x + 1

• Go to 1 on the y axis and go up 1, over 2 units. The line is also dotted because < is not equal to (≤). Since it is less than, <, you will shade below the line you make.

Answer is:

Here is the final graph.

The red line is y > -1-1/3x, the blue line is y < 1/2x + 1.