Question

A system of linear inequalities is shown below:

x + y ≥ 4
y < 2x - 3

Describe the steps to graph the solution set to the system of inequalities. (10 points)

Answer 1

im horrible with these types of questions

Answer 2

The first thing I tell my students about these is to first temporarily replace the inequality signs with = signs, simply for the purposes of solving for y and graphing the lines. We will put them back in later. For the first one, we will rename that x + y = 4. Solving this for 4 gives y = 4 - x. Are you familiar with the slope-intercept form of graphing? The y-intercept is 4 and the slope is negative 1. We will graph that on a poorly drawn graph here!
That's that line. The other one is y = 2x - 3. The y-intercept is -3 and the slope 2.
That's the other one poorly graphed. Now let's graph them on the same plane using the signs this time.
Notice that the dotted line goes with the "less than" and the solid line goes with the x + y is greater than or equal to 4. Now we will pick points to satisfy these equations. With the first one, test the easiest point ever, (0, 0). Fill (0, 0) into the equality statement and see if it's true. For x + y greater than or equal to 4: 0 + 0 is greater than or equal to 4? No, so the points on the other side of the line satisfy the statement. I'll draw that in a sec. For the other one, y < 2x - 3, do the same with the point (0, 0). 0 < 2(0) - 3? No. So the other points satisfy the statement.
Where the two "shaded" sections overlap is the solution!