Identifying and verifying a solution to a system
About this video
A system of two lines, y = -2x - 2 and y = -1/4x + 5, is graphed, and the solution is where they cross. From the graph the crossing point looks like (-4, 6). The video checks this by putting x = -4 into both equations; each gives y = 6, so (-4, 6) is on both lines and is the solution.
You'll be able to
- find the solution of a system of linear equations from where the graphs intersect.
- verify a solution by substituting it into both equations.
Key words
- system of linear equations
- Two or more linear equations considered together.
- solution of a system
- An (x, y) pair that makes every equation in the system true.
- verify
- Check that an answer really works by substituting it back in.
Transcript
- [Instructor] We're told the system of linear equations below is graphed on the coordinate grid. So we can see the graph of y is equal to -2x - 2 in blue here. And then, y is equal to -1/4x + 5 in brown here. And what I want you to first do before I do it with you is see if you can visually think about what the solution is to this system, so an x and y pair that satisfy both of these equations.
And then, I want you to verify that it is indeed the solution. All right, now when I visually inspect it, it looks like this point right over here is on both lines. And if I eyeball it, that looks like the point x is equal to -4 and y is equal to 6, so -4, 6. But let's verify that that indeed is a point on both of these lines.
And to do that, let's see what y is equal to in each of these when x is equal to -4. So in that first one, and maybe I'll do it in that same color just to make or a close color, so if I say y is equal to -2 times -4 - 2, that's equal to +8 - 2, which is indeed equal to 6.
So for this blue line, when x is equal to -4, y is indeed equal to 6. Now let's also do it for this brownish looking line. So there, y is equal to -1/4, and here our x is -4. And then, we're gonna have + 5. And so y, so here we have -1/4 times -4 is +1 + 5 is indeed equal to 6.
So that point -4, 6 is indeed on both lines.
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