 This recording is going to show you how to evaluate expressions and equations. So for this first one, we have 4x plus y, and we want to know what it's equivalent to when x is 1 and y is 2. So we would say 4 times our x, which we want to be 1, plus our y, which is 2. Well 4 times 1 would be 4 plus 2, so when x is 1 and y is 2, 4x plus y is equivalent to 6. Let's try it with some different values. So I have 4, and I want to put 0 in for x this time, and then we add our y, which is 5. Well 4 times 0 would be 0 plus 5, 4x plus y, when x is 0 and y is 5 would be 5. This time we have a fraction, but we do exactly the same thing. When x is 1, and actually there is no y here, so we can just kind of cross that out, and just say that 1 plus 1 on the top divided by our x, which is 1, minus 1 on the bottom, would give us 2 divided by 0, and when you divide by 0, then we know that there is no answer. It's undefined, okay? If it had been switched around the other way, and the 0 had been on top, if it had been 0 divided by 2, then this one would have given us 0. But when we divide by 0, we have no solution or no answer. Now let's try x equals 0. Again, we don't have a y, so we can cross that out, and we can say that x is 0 plus 1 divided by x again being 0, minus 1, and that gives us 1 over negative 1, and we haven't really talked about these kinds of numbers yet, but this actually would be equal to negative 1. That's kind of a bonus question, all right? We'll make that a bonus. Now we have b squared minus 4ac, so let's plug in. We have three different variables, but we just plug and chug, so b is 3, and we're going to have to square that, and then minus 4, and then times a, which if we see, that says 2, times c, which we see is 1. So order of operations tells us that we have to do the 3 squared first, so 3 squared would be 9, and then we have our minus 4 times 2 times, I'm just going to write these like this until we get the numbers in there. So now order of operations says we have to multiply these two, so we have our 9, and now it's going to be minus 4 times 2, which is 8 times 1, and we still have a multiplication right here, so we still carry our 9, and then it will be minus 8 times 1, which is 8. So now we have 9 minus 8, which is going to be 1. All right, so now we have an equation, but we do the same thing. We just plug in for the variable, do our order of operations and see if we get a true or false statement. So we start out with a y, and we know that to be 3, it's asking us, is y equal to 3, what is the solution? And then we're going to square that, and then plus 3 times our y, which is 3, and then minus 6, is it equal to 12? Order of operations tells us we have to do 3 squared first, so we have 9, and then all our exponents are done, so we can do our multiplication next, so 3 times 3 is 9, and then minus 6 equal to 12. And now we just work across left and right in our addition, 9 plus 9 is 18, minus the 6, and is that equal to 12? 18 minus 6 is equal to 12, and sure enough, that's equal to the 12 on the other side, so it is a solution. Let's try it now with x equal 5 for this equation. Order of operations tells us that we have to do our parentheses first before we do anything else, so we still have 4 times 5 minus 2. But inside here, 5 plus 1 is going to give us 6, and then that will still be equal to our 5 plus 2. Now we're ready to do multiplications, so we have 4 times 5, which is 20, and then minus, because we can't subtract yet, but we've got another multiplication right here, and 2 times 6 is going to be 12, equal to 5 plus 2, we still haven't added or subtracted. Now we're finally ready to do that, so on this side, 20 minus 12 will be 8, equal to 5 plus 2, let's get a new color, which is 7, and it's not a solution, because 8 is not equal to 7.