The variables? Well, like in the problem weĭid a little bit earlier in the video, what if we were to This equation that will help us eliminate one of There something we could add or subtract to both sides of You're going to add- let's focus on this top equationĪdd to both sides of this equation that'll help us eliminate one of the variables? Or let me put it this way, is So how can we do this? Remember, with elimination, Hard to eyeball things with the graphing. Of the techniques we've seen so far- substitution,Įlimination, even graphing, although it's kind of What is the cost of each candyīar and each Fruit Roll-Up? And we're going to solve Peter also buys 3 candy bars,īut could only afford 1 additional Fruit Roll-Up. Statement tell us? Nadia buys 3 candy bars, so theĬost of 3 candy bars is going to be 3x. Let's let x equal cost of candyīar- I was going to do a c and a f for Fruit Roll-Up,īut I'll just stick with x and y- cost of candy bar. What is the cost of each candyīar and each Fruit Roll-Up? So let's define some Peter also buys 3 candy bars,īut can only afford 1 additional Fruit Roll-Up. Nadia buys 3 candy bars and 4įruit Roll-Ups for $2.84. Our newly found skills to tackle a word problem, our 5 times 7/2 is 35 over 2 minusĤ times negative 2, so minus negative 8. So let's verify that it also satisfies this bottom equation. Is x is equal to 7/2, y is equal to negative 2. Divide both sides byĤ, and you get y is equal to negative 2. Thought up here- 4y is equal to negative 8. Or we could write that- let'sĬontinue up here- 4y- I'm just continuing this train of
Which is the same thing- well, I'll write it outĪs negative 16 over 2.
Left with a 4y, because these two guys cancel out.
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So this is going to be 21 overĢ plus 4y is equal to 5/2. Times 7 over 2- I'm just substituting the x value weįigured out into this top equation- 3 times 7 over 2, You could do it with theīottom one as well. This back into either of these two equations. And you divide both sides by 8,Īnd we get x is equal to 28 over 8, or you divide the When I looked at these twoĮquations, I said, oh, I have a 4y, I have a negative 4y. And then what is 4y minus 4y? And this was the whole point. This quantity and this quantityĪre the same. Things to both sides of the equation? And my answer would be no. On the right-hand side, you'reĪdding 25.5 to the equation. Wait, on the left-hand side, you're adding 5x minusĤy to the equation. The equation, you have to do to the other side. You would get Ax plus By, plusĭ is equal to C plus D. Because D is equal toĭ, so I won't be changing the equation. So I could, for example, I couldĪdd D to both sides of the equation.
Same thing to both sides of the equation. Want to do something to this equation, I just have to add the Really, any equation- Ax plus By is equal to C, if I Hold on, how can you just add two equations like that? And remember, when you're doingĪny equation, if I have any equation of the form- well, This to the left-hand side, and add that to the We were to add 5x minus 4y to the left-hand side, and addĢ5.5 to the right-hand side? So if I were to literally add Just added this equation to that equation? What I mean by that is, what if And it's probably not obvious,Įven though it's sitting right in front of your face.
That might eliminate one of the variables? And then we would have oneĮquation in one variable, and we can solve for it. But is there anything that weĬould add or subtract to both sides of this equation Or subtract to both sides of this equation? Remember, any time you deal withĪn equation you have to add or subtract the same Or subtract- let's focus on this yellow, on this topĮquation right here- is there anything that we can add We like to eliminate one of the variables. So how can we proceed? We saw in substitution, Represent the solution sets to both of these equations. This would be the intersection of the lines that Value that satisfies both of these equations. Let's say I have the equation,ģx plus 4y is equal to 2.5. More methods for solving systems of equations.
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