When you’re given a system of inequalities and asked to solve, you still start out by solving each equation for y. So let’s do that, let’s work with our first equation here and solve for y.

So this equation says three x minus two y is less than or equal to four. The first thing I will do is I will subtract three x from both sides. And I will get negative two y is less than or equal to negative three x plus four. Next is we divide by negative two. Now, what happened to my sign, my inequality sign when I divide by a negative, it flips. It changes. So we have three halves x here, minus two. So there’s our first equation.

Let’s try the second one. We have x plus two y is less than two. So we’ll subtract x from both sides and we have two y is less than negative x plus two. Divide everything by two and we have y is less than negative one half x plus one. So there’s our second equation.

So now we have to graph each one of these. So let’s first figure out what is our borderline going to be here? Is it going to be solid or is it going to be dotted? Remember, if it has this equals sign, that means it is going to be solid. Our second equation, however, doesn’t have that so that means it is going to be dotted. After we graph the borderlines, we then have to shade. Now, my method of figuring out how to shade is a little bit different than you learned on the other slide, so you might want to write this down as well. I go by saying if my y is by itself on the left side, my inequality sign tells me where to shade. For instance, my y is by itself on the left hand side here, my inequality sign says greater than, since it’s greater than, that means bigger, you shade above.

Let’s look at the other one. My y is by itself on the left side my sign says less than, so that means I shade below it. And that method only works when the y is by itself on the left side of the inequality. So let’s go ahead and graph this. Let’s graph our first one. We start at negative two, we go up three, over two. I like drawing three points, that just makes it more accurate. This is a solid line. Draw a solid line. Just like that.

And we need to shade above it. So that means everything above this line over here so we will shade all of this right here. So that first one is done. Let’s draw our second one. I start at positive one and I go down one and to the right two, now, this one is dotted, so we have to draw a dotted line. All right, so there is my dotted line. And this one says to shade below. So that means I’m going to show underneath the line, below the line. So everything right here.

Now, there’s the graph for the second equation. Now what happened when I started shading in to here notice how it changed colors and I did that for a reason because the answer for the systems of equations is where their two shadings overlap. So where this yellow went into the blue and it turned into green. This right here, is the answer for our systems of equations. It’s all this right here. So you would darken that section right there.