Question

Graph the solution to the following system of inequalities.y>3x+7y≤−3x-8

Answer 1

Step 1. Graphing the first inequality.

The first inequality is:

`y>3x+7`

to graph this, we need to graph the line 3x+7, which compared with the slope-intercept equation

`y=mx+b`

where m is the slope and b is the y-intercept, the line

`y=3x+7`

is a line with a slope of 3 and a y-intercept at 7:

SInce the inequality is:

`y>3x+7`

The solution just for this inequality are the values greater than the red line, but not including the red line so we represent is a dotted line and a shaded part above:

Step 2. Graph the second inequality.

The second inequality is:

`y\le-3x-8`

As we did with the first inequality, we graph the line -3x-8 first.

comparing -3x-8 with the slope-intercept equation:

`y=mx+b`
`y=-3x-8`

we can see that the slope m is -3 and the y-intercept b is -8. This line is shown in blue in the following diagram along with our results for the previous inequality:

Since the inequality form is:

`y\le-3x-8`

We shade the values below this blue line:

The final solution will be the intersection between the red part and the blue part: