Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate system and finding all points of intersection. Check all solutions in both equations. So if X + y equal -3, we get Y equal negative X -, 3. So we have a slope of -1 and AY intercept at the .0 negative 3. So we're going to go down zero -3 we're going to go down one right one or up one and left one and put in our line. The second equation is equation of a circle. The center is at -6 negative 6 and the radius is sqrt 45, which is 3 root five. Well, sqrt 45 is in between sqrt 36 and sqrt 49. So we know that it's going to be in between 6:00 and 7:00. So we're going to go to -6 negative 6 for our center, and then we're going to do in between 6:00 and 7:00, closer to seven and six to draw on our radius. Now they're asking us to do this by graphing. So it looks like we're going to have -3 zero and zero -3 as our two solutions to check. We want to put it in both equations. So if we start with -3 zero, we can see that that checks in both equations, and if we go to zero -3, we can also see that that checks. Now if we wanted to look at this algebraically, X + y equal -3 and X + 6 ^2 + y + 6 ^2 would equal 45. We would take that top equation and solve for one of the two variables. Doesn't matter which. Let's go ahead and solve for Y. So we get y = -X -, 3. Now if we substituted into the other equation, we'd have X + 6 ^2 + -X - 3 + 6 ^2 equaling 45. So here we'd end up with X ^2 + 12, X plus 36. If I foil it out here, we'd end up with X ^2. That's going to end up being a +3. So a negative six X + 9 equaling 45 X squared, and X ^2 is 2 X squared 12X and -6 X is going to give us +6 X 36 and nine is 45, and there's a 45 on each side, so that's going to equal 0. If we factor out a 2X, we get X + 3 equaling 0. So we can see X is 0 and X is -3. If X is 0, we can find our Y by negative X -, 3. So when X is zero -0 -, 3 would give us -3 for our Y. When X is -3 negative, negative of -3 -, 3 would give us 0.