How to Solve a System of Linear Equations By Graphing 8 EE C 8

hi welcome to the magic of math today my video Lesson is on graphing system of linear equations our objectives today are that you will solve system of linear equations by graphing and that you will learn how to check your Solutions here's the question I'd like you thinking about today as proceed through the lesson how can you use what you know about graphing line to solve system of linear equations let's review some vocabulary so system of linear equations is set of two or more linear equations in the same variables in this video we're only going to use system as two equations so here's an example of system equals negative 3x subtract 8 is 1 linear equation and then equals one half subtract 1 is second equation so together these two form set that form system of linear equations our second vocabulary word solution of system of linear equations in two variables is an ordered pair that is solution of each equation in the system the solution of linear equation is point or ordered pair of an intersection of the graphs of the equation so lot said here so here's our coordinate plane we're going to show you the graph of the first equation that's in blue equals negative 3x subtract 8 and then in Orange the second equals one-half subtract one so I've just graphed these two lines and the point where they intersect is our solution so negative 2 negative 2 is our ordered pair and that is the solution of our system of linear equations and this point is the only point where they will intersect and it is also the only ordered pair that is solution to each of these linear equations in the system now it's your turn would like you to pause the video here and determine what the solution is of this graph system of linear equations so there are two linear equations graphed on this coordinate plane pause determine the solution and come back and hit play when you're ready welcome back so our solution is where they intersect which is right here so when you start at the origin and you go to the left and then you go up we're going to go one two three four so that's negative four one two three so the point of intersection is the ordered pair negative 4 3 and that is the solution to our system of linear equations again it is the only point on both lines that is solution to the linear equation as well as the system here are the steps for solving system by graphing step one you're going to graph each equation in the same coordinate plane step two you're going to identify the ordered pair where the two lines intersect and step three you're going to check the ordered pair from step two by substituting the and values this ordered pair into each equation to verify it is solution to both equations so three simple steps I'm going to model those steps for you here and we're going to solve this given system by graphing so step one we're going to graph each equation in the same coordinate plane so I'm going to start by graphing our blue equation here our y-intercept is negative 8 so go and plot point at negative 8. my slope is negative 3. so I'm going to rise one two three and run negative one so run one so my slope and connect the points is negative so have to be falling left to right so again 1 2 3 and 1 Direction has to be negative so if go up have to go left or can go down which is negative and right positive so that's our blue line now let's graph our orange linear equation our y-intercept is negative one so I'm going to plot point in negative 1. then my slope is one half so I'm going to rise 1 and Run 2 and plot my second point and then draw my line so there's my system step two is to identify the ordered pair where the two lines intersect so that's right here so plot my point and that is negative 2 negative two step three is to check that this ordered pair is actually solution to both and that didn't make mistake by graphing so I'm going to start with my first equation and I'm going to come up here and check so I'm going to replace this with negative 2 and I'm going to replace this with negative 2 because this is so again replace the with negative 2 and the with negative 2 and got that from here this ordered pair negative 3 times negative 2 is positive 6. so negative 2 does it equal 6 subtract 8 that's what we're asking 6 subtract 8 is 6 add negative 8 which is negative 2 and it checks but now we need to check to make sure it's solution of the second equation as well so again I'm going to replace with this negative 2 and with this negative 2. so let's come over here negative 2 equals one-half times negative 2 subtract 1. so we multiply first one half times negative two half of negative two is negative one negative one subtract one is negative one add the opposite so negative one add negative one is negative two and it checks so we know that that is the true solution to this system of linear equations now it's your turn would like you to pause the video now and solve this system by graphing don't forget to check your solution into both equations please pause and come back when you're ready welcome back so we're going to begin by graphing step one is to graph each so I'm going to graph this one in blue so my y-intercept is 3. one two three my slope is two I'm going to rise two and run one and plot my point connect the points with line graph our second one with an orange line my y-intercept is negative three one two three plot my point my slope is negative four so have two choices here could fall instead of rising could go down one two three four and run positive one and plot point or could rise one two three four and run in negative Direction and plot point and connect my line so my line is falling left to right because have negative slope the blue line is rising left to right because have positive slope all right step number two now that I've graphed this is to identify the point of intersection which is right here so that point is negative one positive one so that's how would write it is negative one is one now my final step step three is to check that this solution is true to both linear equations so let's check we're going to replace with positive one and with negative 1. so here we have it we're checking the blue equation first when is one is negative 1 is that true 2 times negative 1 is negative 2 negative 2 plus 3 is positive one and it checks now we have to check the second equation so I'm going to replace with one and with negative 1. so when we write it it looks like this we're going to multiply negative 4 times negative 1 which is positive 4 and 4 subtract 3 is 1 and it checks therefore we know that the solution to this system is the ordered pair negative 1 1. your turn would like you to solve this system by graphing don't forget all three steps and check your Solution please pause now come back when you're ready welcome back so we're going to start by graphing so first one here our y-intercept is zero because it's one half plus zero so I'm going to plot point at the origin my slope is one half so I'm going to rise one and run two and plot my point and connect my points with line let's graph the orange one here our y-intercept is negative 2. so plot point on the y-axis at negative 2 and our slope here is one that invisible coefficient is one One so I'm going to rise 1 and Run 1 and plot point and connect my line now need to do step two which is to identify the point of intersection which is right here and that point is one two three four up two so the ordered pair is positive four positive two so now need to check my solution so I'm going to check by replacing the with 4 and the with 2. so let's start with the blue so when is 2 and is fours is true one-half times four half of four is two it checks now let's plug it into the second equation when is 2 is 4 it would look like this four subtract 2 is 2 and it checks therefore we know that the solution of the system is the ordered pair 4 2. all right your turn without graphing determine the solution of the system of linear equations here's your system and here are your four possible solutions only one can be true go ahead and pause now and come back when you're ready welcome back so to get to the answer our solution what we're going to do is use our step three which is to check our solution so let's start with if go and check I'm going to replace with negative 2. and with negative 3 in both equations so the first one is when is negative 3 and is negative 2 is this statement true 2 times negative 2 is negative 4. negative 4 subtract 1 negative 4 add the opposite would give me negative five that is not true therefore can stop because if it's not true for the first it's not going to be true for the second it doesn't matter if it's true for the second because it has to be true for both all right let's move on to Choice and check so we're going to replace with 3 and with 2. so when we do that this is what it looks like 2 times 2 would be 4 4 subtract 1 is 3 it checks so it works for the first equation let's see if it works for the second we're going to take 3 in for and replace with 2. so it looks like this negative negative two plus five is written like this negative 2 plus 5 is 3 and it checks so we know that is solution so we have our solution let's just talk about for minute if we plug in negative 3 for that would be negative 6 negative 6 subtract 1 is negative seven not two so we know that it couldn't be let's try this one quick three times two is six subtract one is five not two so it doesn't check so our solution here is thanks for joining me today on learning how to graph system of linear equations hope you'll come back soon at the join me at the magic of math where we continue to master math one video at time have great day