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Name: Class: M8U5: Notes & HW #7 Practice Solving Systems Date: Warm Resolve each system using any method 9 × 3 y 24 1. 7 3 y 20 4 × y 6 2. 3x 2 y 21 Example A: A fashion designer makes and sells

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Hello and welcome to another common core algebra 1 lesson by emathinstruction my name is Kirk Water then today we're going to be doing unit number five lesson number seven solving systems of inequalities before we being let me remind you that you can find a worksheet that goes with this video along with a homework assignment by clicking on the video's description or by visiting our website at WWE math instruction calm as well don't forget about the QR codes on the top of every worksheet use your smartphone or tablet to scan those codes and bring you right to these videos okay, so previously we've learned about systems of equations and systems of inequalities we've also learned about how to graph linear inequalities in two variables today what we're going to be doing is combining all of those to graph the solution sets of systems of inequalities all right but first let's jump in an exercise one take a look at a system of inequalities alright and try to figure out whether particular points are solutions to those systems alright so we want to do is we want to figure out if the point 3 comma 8 is a solution to that system now it doesn't matter whether it's a system of equality or a system of inequalities or a mixed up system the plain fact is a point is a solution to a system if it makes all the equations or in this case inequalities true so let's take a look and letter an if I take that first inequality X plus y is greater than 10, and I put 3 in for X and I put 8 in for Y right I'll get 11 is greater than 10 and that's true if I take the next one Y is greater than or equal to 3x minus 5, and I put 8 in for Y and I put 3 in for X I'll get 8 is greater than or equal to 9 minus 5 8 is greater than or equal to 4 that's also true because I have those two true the answer is yes so at the end of the day in letter C we're going to graph the solution set to this system of inequalities 3 comma 8 better be in there when I pause the video and see if the point 5 comma 9 is a solution to the system of inequalities alright let's go through it hopefully this time you found that the answer was no but let's take a look I have X plus y is greater than 10, so I'll put 5 plus 9 in there greater than 10 14 is greater than 1000 that's true let's try this one Y is greater than or equal to 3x minus 5, so I'll put 9 in there and open 5 in there 3 times 5 is 15 minus 5 9 is greater than or equal to 10 and that's false it doesn't particularly matter that this one's true the plain fact is if any of them are false the answer is no so just as we pointed out in letter a when we ultimately graph this thing that point shouldn't be in the solution set so let's let's remember head graph inequalities, and actually I'm going to start with this one Y is greater than or equal to 3x minus 5 because it's the easier one remember what we're going to do is we're actually going to first graph this equation y equals 3x minus 5 it should be pretty easy right we have a y-intercept of negative 5,...

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