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# Are all second degree linear equations conic sections?

Updated: 9/23/2023

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Q: Are all second degree linear equations conic sections?
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### What are the differences of linear and non-linear equation?

Linear equations have a variable only to the first degree(something to the power of 1). For example: 2x + 1 = 5 , 4y - 95 = 3y are linear equations. Non-linear equation have a variable that has a second degree or greater. For example: x2 + 3 = 19, 3x3 - 10 = 14 are non-linear equations.

### What is the best way to solve second degree equations?

The answer depends on whether the equations are second degree polynomials, second degree differential equations or whatever. The methods are very different!

### The standard conic section are described today by Linear equation Bi-quadratic equations Quadratic equations Cubic equations?

The standard of conic section by linear is the second order polynomial equation. This is taught in math.

### What has the author Avron Douglis written?

Avron Douglis has written: 'Ideas in mathematics' -- subject(s): Mathematics 'Dirichlet's problem for linear elliptic partial differential equations of second and higher order' -- subject(s): Differential equations, Linear, Differential equations, Partial, Dirichlet series, Linear Differential equations, Partial Differential equations

### What is the meaning of a system of linear equation that are dependent?

It means that at least one of the equations can be expressed as a linear combination of some of the other equations. A linear combination of equations is the addition (or subtraction) of equations. And since an equation can be added several times, it includes multiples of equations. For example, if you have x + 2y = 3 and 2x + y = 4 Then adding 2 times the first and 3 times the second gives 8x + 7y = 18 This is, therefore, dependent on the other 2. If you have n unknown variables, there will be a unique solution if, and only if, you must have a set of n independent linear equations.

### Can you patent math work?

Higher-level mathematical concepts, such as entirely new methods of calculation, may be patented. For example, this is the abstract of a patent application being reviewed at the moment: A method for obtaining an estimate of a solution to a first system of linear equations. The method comprises obtaining a second system of linear equations, obtaining an estimate of a solution to said second system of linear equations, determining differences between said first and second systems of linear equations, and determining an estimate of a solution to said first system of linear equations based upon said differences and said estimate of said solution to said second system of linear equations. In the language of the various laws, this would be called a "process," which the statute degines as "a process, act, or method." Also according to the law, the process must be useful and novel. It's worth noting, though, that case law has defined that "laws of nature, physical phenomena, and abstract ideas are not patentable subject matter."

### Complex roots occur in conjugate pairs?

Not for all types of equations. But always in second degree equations they do. Consider a third degree equation with 3 different roots. Obviously, one of the roots can not be in a pair.

### What is consistent and dependent?

The terms consistent and dependent are two ways to describe a system of linear equations. A system of linear equations is dependent if you can algebraically derive one of the equations from one or more of the other equations. A system of linear equations is consistent if they have a common solution.An example of a dependent system of linear equations:2x + 4y = 84x + 8y = 16Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 16, which gives 16 = 16.No new information was gained from the second equation, because we already knew 16 = 16, so these two equations are dependent.An example of an inconsistent system of linear equations:Because consistency is boring.2x + 4y = 84x + 8y = 15Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 15, which gives 16 = 15.This is a contradiction, because 16 doesn't equal 15. Therefore this system has no solution and is inconsistent.

### How is a system of 2 linear equations have no solution?

The pair of equations: x + y = 1 and x + y = 3 have no solution. If any ordered pair (x,y) satisfies the first equation it cannot satisfy the second, and conversely. The two equations are said to be inconsistent.

### Do quadratic equations have exponents?

Yes. A quadratic is a second degree equation, one in which the highest power is 2 (i.e. squared).