Solutions to 2-variable equations: substitution (old)

0:00Is 3 comma negative 4 a solution to the equation 5x plus 2y is equal to 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 just to substitute x is equal to 3 and y equals negative 4 into this and see if 5 times x plus 2 times y does indeed equal 7.

0:21So we have 5 times 3 plus 2 times negative 4. This is equal to 15. 15 plus negative 8, which does indeed equal 7. 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.

0:44It is. Now, another way to do it, and I'm not going to go into the details here, is you could 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.

0:59If 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 and so you could very precisely determine whether it's on the line.

1:13If 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 had to do in this example. So it definitely is a solution to the equation.