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# Systems of equations with elimination: x+2y=6 & 4x-2y=14

CCSS.Math:

## Video transcript

use elimination to solve for x and y and they give us two equations here X plus 2y is equal to 6 and 4x minus 2y is equal to 14 so the salt to solve by elimination what we do is we're going to add these two equations together so that one of the two variables essentially gets eliminated gets canceled out and what we could do right here we see we have a plus 2y here we see we have a negative 2y right over here so clearly if we added these two together the Y's would cancel out and so that's what exactly what we're going to do we're going to add the left side of this equation to the left side of this equation and the right-hand side of that equation to the right-hand side of the bottom equation and just to make it clear that this should make sense is we're just using both of these constraints whenever you learn about any type of equation so when if I have X plus 2y is equal to 6 you learned early on in algebra that it's you can manipulate this equation in any way as long as whatever you do to the left-hand side of the equation you do to the right-hand side if this is equal to that the only way that the Equality will still hold is whatever you do to this whatever you add to this or so multiply it by you also do to the right-hand side so when we're adding these two equations that's exactly what we're doing we could say hey let's add 14 to both sides of this equation so you could add 14 on this side you could add 14 on that side that wouldn't be anything new but the second equation right here tells us that 4x minus 2y is the same thing as 14 so instead of adding 14 on the left-hand side I could add 4x 4x minus 2y when we're adding these two equations we're really just adding the same thing you could view it as we're starting with this equation and then we're adding the same thing to both sides on the right hand side it looks like we're adding 14 to the 6 on the left hand side it looks like we're adding 4x minus 2y to whatever's on the left hand side but the second constraint tells us that 14 and 4x minus 2i are the same thing so we're adding the same thing to both sides so with that said let's just do it so the left hand side if we add it up we have X plus 4 X is 5x and then the 2y cancels out with the negative 2i and then on the right hand side we have 6 plus 14 6 plus 14 is 20 so we're left with one equation with one unknown 5x is equal to 20 we can divide both sides by five and we are left with X is equal to four now we can go back and substitute in x equals four into either of these equations to solve for y so let's use this top one so we have 4 plus 2y is equal to 6 we can subtract 4 from both sides so then we get 2y is equal to 2 divide both sides by 2 we get Y is equal to 1 so the solution the X's and Y's that satisfy both of these equations are X is equal to 4 and Y is equal to 1 so this is the solution for this system or this coordinate would be the point of intersection of these two lines and we can verify it lets verify that when we put X is equal to 1 sorry X is equal to 4 and Y is equal to 1 of this first equation it satisfies it so we have 4 plus 2 times 1 that's 4 plus 2 that does indeed equal 6 and then in the second equation right over here you have 4 times 4 minus 2 times 1 minus 2 times 1 this is equal to 16 minus 2 which does indeed equal 14 so it definitely does satisfy both of these equations so we're done X is equal to 4 and y is equal to 1