Visually verifying a solution to a system
About this video
Two lines, y = -x - 7 and y = 1/2x - 1, are graphed. At x = -8 the blue line has y = 1 and the brown line has y = -5. Because the y-values are different, the lines don't meet there, so x = -8 is not a solution of the system.
You'll be able to
- read the y-value of a line at a given x from a graph.
- explain that a solution needs both lines to have the same y-value at the same x.
Key words
- system of linear equations
- Two or more linear equations considered together.
- solution
- An x and y that make both equations true; on a graph, where the lines intersect.
- intersect
- Cross or meet at the same point.
Transcript
- [Instructor] We're told the system of linear equations below is graphed on the coordinate grid. Okay, we see that. Then, it says: What is the value of y equals -x - 7 when x is equal to -8. So the graph y equals -x - 7, that's this blue line here, and they tell us, right?
That the point -8, 1 is on that line. So when x is equal to -8, y is equal to 1. So we could type that in. And then, they ask us: What is the y-value of the bronze line or the brown line here, y is equal to 1/2x - 1 when x is equal to -8. So we don't even have to compute it.
We see when x is equal to -8, we get y is equal to -5, so we put -5 there. And then, they say: Is x equal -8 a solution? Well, the only way that x equals -8 would be a solution is if the y value of those lines when x equals -8 were the same, but they're clearly not.
And in fact, we would see it visually. If it was a solution, the two lines would intersect at that point but they don't. There's actually two different points here. They don't overlap. So this is not a solution and we're done.
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