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Hi everybody um we are back for a whole new unit whew this unit definitely one of my favorites you might not agree, but that's working were going to go through and yeah were doing were going to go through and see what happens okay this is unit five systems of equations and inequalities and today well look for the next like three days were focusing on systems of equations and then well switch gear same equality so lets go ahead and get started all right, so first vocab system of linear equations is a group of two or more linear equations with the same solution okay so when we talk about linear equations so like y equals MX plus B or standard form ax plus B y equals C those are our linear equations are most likely going to deal with here and to find a solution to that system just like finding a solution to any linear equation they're looking for well actually I was curious definition so a solution to a system of linear equations just like a solution to a linear equation is an ordered pair that makes all equations in the system true so that's the only difference is that it has to work for everything in that system to tell if its true or not we take that x and y from the ordered pair, and we plug it into the equation when we simplify we just get a true statement, so that's how we check to see if a solution is true just like how we checked to see if we are able to like when we solve for x or something we check to make sure it was actually the solution by plugging it back in to see if it actually gave us a true statement so same thing here because an ordered pair has an x and y that's why it's not a solution so were talking about linear equations solutions our ordered pairs okay autograph it's the ordered pair where all the equations in sect, so they all like cross at the same point that's the solution to the system, but algebraically it's just the one that works when you plug it back, and it works for everything okay sorry sounds very, very wordy let me move this, so you can see there you go and if you need you pause the screen, so you can copy it all down but yeah alright, so there's a little more into systems that you want to know its just kind of like the general information of systems of equations there are three different kinds of systems all yeah three different kinds but like two categories they can be in consistent systems our systems of equations that have at least one solution okay so those the ones where you will have an answer for inconsistent systems are ones that have no solution okay and yes so we have no solutions yes it is possible to get infinite solutions as well okay so the two kinds of consistent systems kind of differentiate this at least one solution, so an independent consistent system there's a system with exactly one solution okay were dependent consistent systems are systems that have infinitely many solutions so just like when you were solving equations when you solve a system you can have the same number of answers one...
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