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A linear equation has a n infinite number of solutions. The coordinates of each point on the line is a solution.
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Why does the discriminant determine the number and type of the solutions for a quadratic equation?
A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.
What common characteristics do linear and nonlinear equations have?
Generally, both types of equation contain an equals sign and some combination of numbers and/or variables. That is the only thing I can think of that is common between all types of nonlinear and linear equations.
What are the three types of possible solutions to a system of equations?
If the equations are linear, they may have no common solutions, one common solutions, or infinitely many solutions. Graphically, in the simplest case you have two straight lines; these can be parallel, intersect in a same point, or actually be the same line. If the equations are non-linear, they may have any amount of solutions. For example, two different intersecting ellipses may intersect in up to four points.
What reasoning and explanations can be used when solving radical equations?
The basic method is the same as for other types of equations: you need to isolate the variable ("x", or whatever variable you need to solve for). In the case of radical equations, it often helps to square both sides of the equation, to get rid of the radical. You may need to rearrange the equation before squaring. It is important to note that when you do this (square both sides), the new equation may have solutions which are NOT part of the original equation. Such solutions are known as "extraneous" solutions. Here is a simple example (without radicals): x = 5 (has one solution, namely, 5) Squaring both sides: x squared = 25 (has two solutions, namely 5, and -5). To protect against this situation, make sure you check each "solution" of the modified equation against the original equation, and reject the solutions that don't satisfy it.
What is an equation with only variables?
There is no specific name. It could be a linear or more complicated polynomial equations, it could be trigonometric, exponential or any one of many other types. It could be a combination of these
How can you tell when an equation in one variable has infinitely many solutions or no solutions?
There is no simple method. The answer depends partly on the variable's domain. For example, 2x = 3 has no solution is x must be an integer, or y^2 = -9 has no solution if y must be a real number but if it can be a complex number, it has 2 solutions.
What are the three types of system of linear equations?
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.
Why does the discriminant determine the number and type of the solutions for a quadratic equation?
A quadratic equation is wholly defined by its coefficients. The solutions or roots of the quadratic can, therefore, be determined by a function of these coefficients - and this function called the quadratic formula. Within this function, there is one part that specifically determines the number and types of solutions it is therefore called the discriminant: it discriminates between the different types of solutions.
What are types of substances which are written in ionic form in an ionic equation?
Substances that are able to be dissociated in ions in water solutions.
What common characteristics do linear and nonlinear equations have?
Generally, both types of equation contain an equals sign and some combination of numbers and/or variables. That is the only thing I can think of that is common between all types of nonlinear and linear equations.
What are the three types of possible solutions to a system of equations?
If the equations are linear, they may have no common solutions, one common solutions, or infinitely many solutions. Graphically, in the simplest case you have two straight lines; these can be parallel, intersect in a same point, or actually be the same line. If the equations are non-linear, they may have any amount of solutions. For example, two different intersecting ellipses may intersect in up to four points.
How many types of solutions of a system of two linear equations in two unknowns can exist?
There is only one type of solution if there are two linear equations. and that is the point of intersection listed in (x,y) form.
What are 5 types of solutions?
There are many different types of solutions. Some examples of different solutions are isotonic solutions, hypertonic solutions and hypotonic solutions.
How do you do Linear and Exponential Equations?
That completely depends on exactly what operation you have in mind. You can "do" several different types of operations to an equation, such as solve it, differentiate it, rearrange it, factor it, or apply the same arithmetic procedure to both sides of it. But you can't "do" the equation.
How many different equation types are there?
Thanks to the contributors at Wikipedia here is the answer...Equations can be classified according to the types of operations and quantities involved. Important types include:An algebraic equation is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.A linear equation is an algebraic equation of degree one.A polynomial equation is an equation in which a polynomial is set equal to another polynomial.A transcendental equation is an equation involving a transcendental function of one of its variables.A functional equation is an equation in which the unknowns are functions rather than simple quantities.A differential equation is an equation involving derivatives.An integral equation is an equation involving integrals.A Diophantine equation is an equation where the unknowns are required to be integers.A quadratic equationTo learn more click on the Wikipedia Link in the sources and references section below.
What are solutions of trigonometric equations?
That means the same as solutions of other types of equations: a number that, when you replace the variable by that number, will make the equation true.Note that many trigonometric equations have infinitely many solutions. This is a result of the trigonometric functions being periodic.
How can you find out how many solutions an equation has?
By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.
