Identifying Solutions of Systems Review | Expressions & Equations | Grade 8
It’S asking us tell whether the ordered pair is the solution of the given system. Now we know a solution is when the two lines intersect at a point and they are giving us this point of negative 2, 1 and it’s our job to plug in those values of x and y, in this ordered pair into these two equations or these two Linear functions, therefore, we can find out if it is truly a function or not. So the first thing that i’m going to do is i’m going to divide um each of these equations up into two um two sides. It makes it a little bit easy and organized, and i have y equals a negative 2x minus three and a y equals x plus three. Now i see that my x value is negative. Two and my y value is positive. 1.. So wherever i see those variables x and y in these linear functions i’m going to plug in those particular numbers. So i see a y and so i’m going to put parentheses and open it up negative 2 times x. So whatever x value is was in which that is a negative 2 i’m going to plug in right here and then i’m going to write the remainder of my problem. So the x value we found out that it goes right by the negative 2 and my y value will be plugged in right here. So now let’s go ahead and simplify.
So if i bring down the 1 equals a negative 2 times, negative 2 gives me a positive 4 and then minus 3.. Now 1 equals 4. Minus 3 is 1., so the answer is yes, it is a function and we know that it is for this particular point. It is on this linear function when the both sides of the equation are equal to each other, so let’s see. If the second side is the same, so wherever i see a y i’m going to open up with the parentheses and the x i’m going to open up with the parentheses plus 3., so here i go i’m going to for the x value i’m going to plug. In a negative 2 for the y value i’m, going to plug in a positive 1., so let’s go ahead and see 1 equals a negative 2 plus 3. it’s the same thing of saying: 3 minus 2, and we see that 3 minus 2 is 1 as well, And so this is a yes, yes, this tells us that this line – and this line the point i should let me put it right here – the point negative two one falls exactly where the two lines intersect, therefore identifying the solution of this system is that point of Intersection all right, let’s try another one and see how we do and see if it is an intersection of or the point of intersection here we go let’s go ahead and take that out pull our new problem in all right.
So now we have the ordered pair 9, 2 and it’s. We want to see if 9 2 is the point of intersection for these two equations and x, minus 4 y equals 11 and i will go ahead and write that down and separate x. Minus four y is equal to not 11 is equal to one let’s see, and then we have 2x. Minus 3y is equal to 3.. We see that our x value is going to be 9 and our y value is going to be 2., so let’s go ahead and replace parentheses with the variables, so we can plug the 9 and the 2 into our equation. So our 9 is our x value. So i’m, going to plug in the 9 right here and the 2 is for the y value. So here we have 9 and then we have negative 4 times. 2 is a negative. Eight is equal to one. Yes, nine minus eight is one, so definitely one equals one. So the answer is yes, so let’s go into the second, because before it can be um, a solution of these two said tell where, if the ordered pair is a solution they have to be, it has to be yes on both of the equations. So here we go two replace the x by parentheses, 3. Replace the y by parenthesis is equal to 3., so 9 is going to fall right in here and 2 is going to be right there.
So two times nine is eighteen negative. Three times two is a negative. Six is equal to three eighteen. Minus six is twelve, does not equal three, so the answer is no. It is not a solution. So what really it’s showing us is that we have two lines and maybe on the graph, and maybe our its point of intersection is something else. But this point nine two could be here on the graph and it’s, not where the two lines meet. It could be on the blue line as well, but it’s, not where the point of intersection is all right guys. I hope this was a quick review for you on how to identify solutions of systems. Um, please check out our channel subscribe like and hit those bell.