Identifying and verifying a solution to a system | Grade 8 (TX TEKS) | Khan Academy

- [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.