Yes and sometimes it can have more than one solution.
Yes and yes. eg x = y + 1 has an infinite number of solutions, and {sin(x) + cos(x) = 2} does not have a solution.
-- 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.
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.
A single equation in two variables is, for example. Its graph is a line, and every point on the line is a solution.
An infinite solution means that are an infinite number of values that are solutions.
If the solution contains one variable which has not been fixed then there are infinitely many solution.
The number of solutions an equation has depends on the nature of the equation. A linear equation typically has one solution, a quadratic equation can have two solutions, and a cubic equation can have three solutions. However, equations can also have no solution or an infinite number of solutions depending on the specific values and relationships within the equation. It is important to analyze the equation and its characteristics to determine the number of solutions accurately.
Yes and sometimes it can have more than one solution.
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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 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.
Yes and yes. eg x = y + 1 has an infinite number of solutions, and {sin(x) + cos(x) = 2} does not have a 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
An identity equation has infinite solutions.
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.
-- 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.