Algebra
Math and Arithmetic

# What is an infinite solution to an equation?

001 ###### 2009-06-26 23:47:56

An infinite solution means that are an infinite number of values that are solutions.

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## Related Questions Yes and sometimes it can have more than one solution. Any equation, such as yours, with two variables (x and y, on your case) has an infinite number of solutions. The equation or a system of equations having infinite solutions is called identity/identities. (a+b)^2=a^2+2ab+b^2 is an identity. It has infinite solutions. The equation is true for all values of a and b. how many solutions does the equation have? 4x+1=5+2(2-4) a. one solution b. infinite solutions c. no solution If the equations of the system are dependent equations, which represent the same line; therefore, every point on the line of a dependent equation represents a solution. Since there are an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 3x + 2y = 8 6x + 4y = 16 If the solution contains one variable which has not been fixed then there are infinitely many solution. It's the equation of a straight line. Every point on the line is a solution to the equation. There are an infinite number of them. A linear equation has a n infinite number of solutions. The coordinates of each point on the line is a solution.  It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers. The equations are consistent and dependent with infinite solution if and only if a1 / a2 = b1 / b2 = c1 / c2. An equation that has no solution is called an equation that has no solution. There are an infinite number of such equations.Here's one of them:2x + 6 = -x(Since the solution is only 1 number, theequation can only have 1 variable.) An equation may have zero, one, or more solutions (this is also true for a system of equations). The equation 2 + x = 5 has only solution, for example. x can only equal 3, so there is one solution. (An example of an equation with more that one solution is x2 = 4. In this case x can equal 2 or -2, so this equation has two solutions. An example of an equation with an infinite number of solutions is x + 6 = 3*2 + x. x can equal any number to make this equation true, so it has an infinite number of solutions. The equation x = x + 1 is an example of an equation with no solutions.)  It's the equation of a straight-line graph. Every point on the line is a solution of the equation. There are an infinite number of them. There are an infinite number of solutions to this equation, some of which are (9,0), (12,2), (15,4), (18,6), (21,8) A single equation in two variables is, for example. Its graph is a line, and every point on the line is a solution.  There is no such pair. The solution to equation 1 and equation 2 is x = 1, y = 1. The solution to equation 2 and equation 3 is x = 1, y = 1. And the solution to equation 1 and equation 3 is any point on the line 3x + 2y = 5 - an infinite number of solutions. The fact that the determinant for equations 1 and 3 is zero (or that they are not independent) does not mean that there is no solution. It means that there is no UNIQUE solution. In this particular case, the two equations are equivalent and so have an infinite number of solutions. it is actually an equation of a straight line. so it will give infinite values of ordered pairs, which are the solution of this equation. Such an equation has an infinite set of solutions. You can solve the equation for one variable, in terms of the other. Then, by replacing different values for one of the variables, you can get different solutions. There are an infinite number of equations with this solution, eg x = 6 - 10; x = 45678 - 45682; x squared = 16 etc etc There are an infinite number of ordered pairs that satisfy the equation. -- If the equation has only one variable (like 'x' or 'y'), and the only power of the variable anywhere in the equation is '1', then the equation has one solution. -- If the variable appears raised to powers higher than '1', then there are as many solutions as the highest power of the variable. -- If the equation has two or more variables, then there are an infinite number of solutions.

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