Systems of nonlinear equations 1 - Engineering Mathematics Video Lecture

Which of the following graphs
represents the solutions
to the system of equations x
is equal to 2 minus y and y
is equal to x squared minus 4.
So essentially, we
want to find the graphs
that represent
these two equations,
and where they intersect
represent the solutions.
So, let's see. y equals
x squared minus 4.
That's going to be
an upward opening
parabola with a
y-intercept of negative 4,
and we see that is the case.
Or I should say the
y-coordinate of its vertex
would be negative 4 right
over there, and also
the y-intercept.
So that looks like this
one right over here.
And this is the only one
that opens like that,
so we can immediately
say that this is probably
going to be the red
one right over here.
But we can verify that this line
right over here is 2 minus x.
So if I were to write this in
traditional slope intercept
form, I could rewrite this
as x is equal to 2 minus y.
Add y to both sides.
We have y plus x
is equal to 2, or y
is equal to negative x plus 2.
So we see the y-intercept is
2, and its slope is negative 1.
So that's indeed this line,
and so the solutions here
are going to be that point and
that point right over here.
Red is what represents
the solutions
to this non-linear
system of equations.