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Systems of nonlinear equations 1 - Engineering Mathematics Video Lecture
FAQs on Systems of nonlinear equations 1 - Engineering Mathematics Video Lecture
| 1. What is a system of nonlinear equations? |  |
Ans. A system of nonlinear equations consists of two or more equations that involve variables raised to powers other than 1, and the equations are not linearly dependent on each other. These equations cannot be solved using direct substitution or elimination methods.
| 2. How do you solve a system of nonlinear equations? | |
Ans. Solving a system of nonlinear equations can be done using various methods such as graphical method, substitution method, or Newton's method. The graphical method involves plotting the equations on a graph and finding the intersection points. The substitution method involves solving one equation for one variable and substituting it into the other equations. Newton's method uses iterative techniques to approximate the solution.
| 3. Can a system of nonlinear equations have multiple solutions? | |
Ans. Yes, a system of nonlinear equations can have multiple solutions. This occurs when the equations intersect at more than one point on the graph. Each intersection point represents a solution to the system of equations.
| 4. Are there any applications of systems of nonlinear equations in engineering? | |
Ans. Yes, systems of nonlinear equations have various applications in engineering. They are used in fields such as control systems, electrical circuits, fluid dynamics, and structural analysis. Nonlinear equations can model real-world phenomena more accurately than linear equations, making them essential for solving complex engineering problems.
| 5. Is it possible for a system of nonlinear equations to have no solution? | |
Ans. Yes, it is possible for a system of nonlinear equations to have no solution. This occurs when the equations do not intersect or when the intersection points are complex or imaginary. In such cases, the system is said to be inconsistent, and there is no common solution that satisfies all the equations in the system.
Text Transcript from Video
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.
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.
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Mar 07, 2025
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