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Video transcript

it's three common negative for a solution to the equation 5x plus 2y is equal to seven so they're saying does X equal three y equal negative four satisfy this equation or this relationship right here so one way to do it is just to substitute X is equal to 3 and y equals negative 4 into this and see if five times X plus two times y does indeed equal seven so we have five times three plus two times negative four this is equal to 15 15 plus negative eight which does indeed equal seven so it does satisfy the equation so it is on the line it is a solution x equals 3 y equals negative 4 is a solution to this equation so we've essentially answered our question it is now another way to do it and I'm not going to go to the details here is you can actually graph the line so maybe the line might look something like this I'm not going to do it in detail and you see if you have a very good drawing of it you see whether the point lies on the line if the point when you graph the point does lie on the line it would be a solution if the point somehow ends up not being on the line that you'd know it isn't a solution but to do this you would have to have a very good drawing and so you and so you could very precisely determine whether it's on the line if you do the substitution method if you just substitute the values into the equation and see if it comes out mathematically this will always be exact so this is all we really have to do all we really have to do in this example so it definitely is a solution to the equation