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Equations_Graphing Method

Added Jun 09, 2020 •

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solving systems of equations by graphing method is system of equations is a set of two or more linear equations for example here we have two linear equations y equals 6x - 11 + -2 x - 3 y equals -7 together these two linear equations are a system of linear equations to solve a system of equation means to find the point of intersection looking at the graph below we see that the two lines intersect at the coordinate to one this is our solution or points of intersection for the system of equations above so when solving systems of equations by graphing method we must follow three simple first we must grasp the first equation then we must grab the other equation and lastly we must identify our points of intersection let's look at example a we have a system of equations y equals negative 3x + 2 + y equals 2x - 3 the first thing I want to do is grab my first equation so let's look at my first equation my wife intercept form I first equation is too so I'm going to plot my point here at 2 and then my slope is negative 3 so I'm going to go down three into the right one down to the right one and I'm also going to go back from my Y intercept and go up 3-2 the last one then I'm going to Simply put a line through each of those this is my first line Y equals negative 3x + 2 I'm now going to go ahead and grab my second temperatures of different color just to help us differentiate between the two so for my second line my Y intercept is at -3 so I'm going to plug my point there on the y-axis at -3 and then I'm going to look at my phone which is 2 and I'm going to go up to across one up two across one of two across one you want to fight at least three or four points go ahead and put a line through each of those points once again so now I have graph both lines in our system of equations here animal a step I need to take is to just identify the points of intersection so basically where do our two lines cross well they crossed right here at and one negative one for my solution for this problem is simply one- one so if I want to verify whether my solution is correct I can do so by taking the X and Y values for my solution and plugging it into one of the two equations from my system of equations I'm going to choose to is my second equation y equals 2x - 3 but you can choose either equation and as long as your solution is correct it should work so I'm going to go ahead and plug in my values so -1 4y equals 2 times my ex value 1 - 3 + -1 equals 2 * 1 which is 2 - 3 and then negative one equal to -1 well -1 is equal to -1 that is true there for this text out so let's go ahead and take look at example be once again I have a system of equations but this time you will notice that both equations are in standard form as opposed to slope-intercept form in our please sample in order to make it easier for us to graph these two equations we want to put them into slope intercept form or y equals MX plus b form so let's go ahead and take our first equation negative 2 x + 3 y equals -9 and we're going to solve for y so first thing we need to do is we need to eliminate anything that's around our variable term so here's our variable m3y so we're going to have to eliminate our -2X by adding two acts to both sides now I have 3 y equals 2x -9 so can we how to delete our wife so we will have to divide both sides by 3 now I have y equals two-thirds x - 3 I have found or put my first equation into y equals MX plus b form now for my next step I must take the second and also put that into y equals MX plus b form so I'm going to go ahead and solve for y once again by subtracting X from both sides now I have why equals negative x + 2 now that I have put both equations into y equals MX plus b form we go ahead and move on to graphing so first let's go ahead our first equation which I'm going to graph and pink here so let's look are Y intercept for a first equation is -3 so I'm going to go ahead and plot a point here at -3 on our way and then my slope is 2/3 so I means I'm going to go up to to the right 3 up to to the right 3 and then from that Y intercept point I'm going to go ahead and go down 2 to the last three as well going to Simply put a line through my point and there we have it we have graphed our first line y equals two-thirds x - 3 now I'm going to go ahead and also graph my second life so my y-intercept for my second line is at 2 so I'm going to put a point 2 on the y-axis and in my slope is negative one so I'm going to go down one to the right one down one to the right one down one to the right one and then again down one to the right one and then I'm just going to put a line straight through each of those point so here's my line Y equals negative x + 2 play dentist by the points of intersection or where these two lines cross looking at this graph you can see there are two lines cross at the coordinate three negative one therefore our solution for this system of equations is three- one once again if we want to verify that our solution is correct we can simply take these two values for x and y and plug them into one of our original equations so let's take a look at our original equations I'm going to plug it into a second equation x + y equals 2 so I have plus y equals to I'm going to plug in my Valley 4X till 3 and then my belly 4y which is -1 equals two and then 3 + -1 is 2 which is equal to 2 of this is true there for that checks out okay so let's go ahead and practice here are two practice problems go ahead and process video on your own on a sheet of paper and then once you have completed both press play and verify that your Solutions are correct okay welcome back let's go ahead and see how you did here are your solution for both problems this concludes our tutorial for father systems of equations by graphing method

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Equations_Graphing Method

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