How to Solve a System of Equations by Graphing Simple Step by Step Tutorial

welcome to premath in this video tutorial we are going to solve this given system of equations by graphing method to get complete understanding of this topic please watch this video till the very end for another practice problem so before we start graphing this system of equations this is what am going to do i'm gonna give these equations different colors and here you can see that at the top equation gave it blue color and the bottom equation gave it red color and here is going to be our action plan or our strategy in order to keep things simple we are going to graph each equation individually that is we are going to make blue and red graph separately that means and then finally we're going to put them together in other words we're going to superimpose these two graphs so let's get started with our graphing process we are going to focus on our blue equation the top one just put it down over here and i'm gonna show you how we're gonna graph this thing the very first step is in order to graph this blue equation let me show you simple way of doing this thing right now want you to do the chart and want you to put down right up here and here and this is what we are going to do first am going to put equal to 0 value and see how much is going to be so wherever you see this simply become 0. so let's simplify now so this is going to simply become 2 times 0 minus equals to 4 2 times 0 is 0 minus equals to 4 so negative equals to 4 and if you switch this sign so is going to be simply negative 4. so that means value turns out to be negative 4. and in the next step this time i'm going to put down equal to 0 value and see what turns out to be so wherever we see we can replace it by zero so let's simplify 2 minus becomes 0 equals to 4 so that is going to become 2x equal to divide both sides by 2 turns out to be equal to two so that means value is two so thus we got two points the first point is zero comma negative four the second point is 2 comma 0. let me put down these points right up here these ordered pairs 0 comma negative 4 and the other point is 2 comma 0 and here is our cartesian plane and we are going to plot these two points 0 negative 4 and 2 0 first am going to plot 0 negative 4 is going to be right up here the other point is 2 0 is going to be right up here so these are two points and as you can see that this point is on x-axis no wonder we're going to call it x-intercept and this point is on y-axis we're going to call it y-intercept and here have nicely plotted them up so this first this point is 2 0 and this one is 0 negative 4. in the next step we are going to connect these two points to get our graph and finally here is our graph the blue graph that is 2x minus equals to 4. and now let's focus on the red equation and put it down right up here plus 3y equals to 9 and now we are gonna graph this one so the easiest possible way is once again we are going to create chart i'm going to put down over here over here and first want to pick value zero if pick value zero wherever you see replace it by zero let's simplify so this is going to become zero plus 3y equal to 9 so that is 3y equal to 9 divide both sides by 3 turns out to be 3. so that means equal to 3 so if is 0 is going to be 3. and in the next step this time am going to pick as 0 and see what value we're going to get so wherever you see replace it by 0 let's simplify that thing so this becomes plus 3 times 0 equals to 9 so and 3 times 0 is 0 equal to 9 so that means turns out to be 9 so that means our value is going to be 9 and value is going to be zero so thus we got two points the first point is zero comma three the second point is nine comma zero and am going to write down somewhere the first point is zero comma three and the second point is nine comma zero now we're gonna plot these points next and here is our cartesian plane and we are going to plot these two points so the first one is 0 3 so 0 3 is going to be somewhere here as you can see the next point is 9 0 is going to be right here as you can see once again make sure that this point is on axis no wonder we're gonna call it x-intercepts that this point is on y-axis we're going to call it y-intercept and here have nicely plotted these points and gave them name 9 0 and 0 3 as their location the next we are going to connect these two points to get graph straight line graph and here is the graph for this red equation plus three equal to nine and here is our final product so on the left hand side you see these two graphs these are individual graphs blue and red and now have put them together super superimpose them and where you see this point three two that is the point of intersection of these two lines and that is our solution so thus our solution turns out to be 3 comma 2 where 3 is our value and 2 is our value in the coordinates and finally here is your assignment can you do this problem on your own now you can take your time you can pause the video luckily have already uploaded this video as well you can go ahead and check it out and see the correct answer thanks for watching and please don't forget to subscribe to my channel for more exciting videos bye