 This video is going to be an introduction to systems to determine what a system is and so a system is two equations with two unknowns We've done one unknown before in equations, but we've never done two unknowns with two equations And when we do those we will have an ordered pair as a solution So we need both an x and a y and that ordered pair that we find has to satisfy both equations So that's what we want to do in these two problems It says determine if the ordered pair is a solution to the system So we just plug and chug into each equation to see if it satisfies both or not If we take the first one we have x which is negative 5 Plus 6 times our y which is negative 1 and that's supposed to be equal to negative 11 Well, this would be negative 5 and then 6 times a negative 1 would be minus 6 Equal to negative 11 and we can see that that's true If we put it into the second equation, we have 2 times our x which is negative 5 Minus our y which is negative 1 and that's supposed to be equal to 4 Well 2 times negative 5 is negative 10 Negative times a negative 1 is going to give us plus 1 and that is not equal to 4 So we have negative 5 negative 1 is not a solution to the system if we take a look at our second example Again, we're going to plug and chug so we plug in x is 5 plus y which is 15 And that's supposed to be equal to 20 and we can readily see that it is equal to 20 So we try the second equation 3 times 5 Which is our x minus the 15 which is our y and we're supposed to equal 0 Well 3 times 5 is 15 and we're going to subtract from that 15 and we definitely get a 0 for an answer So 5 15 is a solution to this second system Well graphing is one of the ways that we can solve systems And so we're going to look at some graphs and see if we can find the solution Now this first red line here that is x plus y equal 5 and the blue line is the 5x minus 3 y equal 1 Well every point on this red line is going to satisfy x plus y equal 5 I could pick any point on that red line and plug it in like 0 5 0 for x plus 5 or y is equal to 5 and we know 0 plus 5 is 5 Every point on this line is going to satisfy that that top equation and everyone on the blue line is going to satisfy the second equation But we want to know what satisfies both equations and that would be right here at our intersection Okay, so this point right here is 2 in the x and 3 in the y So 2 3 and let's just double check 2 plus 3 is equal to 5 and that satisfies the top equation and 5 times 2 Minus 3 times 3, which is the y is equal to 1 10 Minus 9 is equal to 1 so we know that it satisfied both equations. Let's look at this example x plus y is equal to negative 10 is Going to be the red line and y is equal to 2x minus 1 is the blue line Again, everything on the red line is going to satisfy x plus y equal negative 10 Everything on the blue line is going to be y equal 2x minus 1. Well, again, we have a system here We want to know where they share the same answer and the same ordered pair and That will be at our intersection and if we look at this intersection if we go up it looks like x is negative 3 And our y if we go across we see that's negative 7 So now negative 3 negative 7 will be our solution plugging it into the top one negative 3 plus negative 7 is negative 10 and negative 7 is Equal to 2 times that negative 3 Minus 1 negative 7 is going to be equal to negative 6 minus 1 so it is true as well