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An old video of Sal checking whether (3,-4) is a solution of 5x+2y=7 by substituting x=3 and y=-4. Created by Sal Khan and Monterey Institute for Technology and Education.
Video transcript
Is (3, -4) a solution to the equation 5x + 2y = 7? So they're saying, "Does x equal 3, y equal negative 4 satisfy this equation, or this relationship right here?" So one way to do it is to substitute x is equal to 3 and y is equal to negative 4 into this and see if 5 times x plus 2 times y does indeed equal 7 So we have 5 times 3 plus 2 times -4 This is equal to 15 plus -8, which does indeed equal 7. So it does satisfy the equations. So it is on the line; it is a solution. x = 3, y = -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 gonna go into details here, is you can actually graph the line. So maybe the line might look something like this, I'm not gonna 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, then you'd know it isn't a solution. But to do this, you would have to have a very good drawing, 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 to see if it comes out mathematically, this will always be exact. So this is all we really had to do, all we really have to do in this example. So it definitely is a solution to the equation