Lesson 12: Solutions to linear equations
- [Voiceover] Which of the ordered pairs is a solution of the following equation? Negative three x minus y is equal to six. What we have to remind ourselves is when we're give an ordered pair, the first number is the x coordinate and the second number is the y coordinate, or the y value. So when they tell us the ordered pair, negative four comma four, they're saying "hey look, if x is equal to "negative four, and y is equal to positive four, "does that satisfy this equation?" And what we can do, is we can just try that out. So we have negative three and everywhere we see an x, everywhere we see an x, we can replace it with negative four. So it's negative three times negative four, minus, minus and everywhere we see a y, we can replace it with positive four. We replace it with positive four. So negative three times x minus y, which is four, needs to be equal to six. Needs to be equal to six. Now is this indeed the case? Negative three times negative four is positive 12. Positive 12 minus four, positive 12 minus four is equal to eight, it's not equal to six. Is not equal, is not equal to six. So this one does not work out. So let's see, negative three comma three. We can do the same thing here. Let's see what happens when x is equal to negative three and y is equal to positive three. So we substitute back in, we get negative three. Negative three times x, which now we're going to try out x being equal to negative three. Minus y, minus y. Y is positive three here. Minus y, gonna do that y color blue. Minus y now needs to be equal to, now needs to be equal, just like before needs to be equal to six. So negative three times negative three. That's going to be positive nine. Nine minus three is indeed equal to six. Nine minus three is indeed equal to six. Nine minus three is six. That is equal to six. This works out. So negative three comma three is an ordered pair that is a solution to this equation.