Yes and yes. eg x = y + 1 has an infinite number of solutions, and {sin(x) + cos(x) = 2} does not have a solution.
None because without an equality sign the given expression is not an equation and so therefore no solutions are possible.
An inconsistent equation (or system of equations) is one that has no possible solutions. That is precisely why we call it inconsistent; there is no solution set that can be substituted for its variable or variables that will make the equation (or system) true.
To determine whether a polynomial equation has imaginary solutions, you must first identify what type of equation it is. If it is a quadratic equation, you can use the quadratic formula to solve for the solutions. If the equation is a cubic or higher order polynomial, you can use the Rational Root Theorem to determine if there are any imaginary solutions. The Rational Root Theorem states that if a polynomial equation has rational solutions, they must be a factor of the constant term divided by a factor of the leading coefficient. If there are no rational solutions, then the equation has imaginary solutions. To use the Rational Root Theorem, first list out all the possible rational solutions. Then, plug each possible rational solution into the equation and see if it is a solution. If there are any solutions, then the equation has imaginary solutions. If not, then there are no imaginary solutions.
Yes, some equations have as many as ten. There is a very rare equations that only two people have seen that has 1 billion solutions.
An equation can be determine to have no solution or infinitely many solutions by using the square rule.
None because without an equality sign the given expression is not an equation and so therefore no solutions are possible.
An equation with a degree of three typically has three solutions. However, it is possible for one or more of those solutions to be repeated or complex.
A single linear equation in two variables has infinitely many solutions. Two linear equations in two variables will usually have a single solution - but it is also possible that they have no solution, or infinitely many solutions.
An inconsistent equation (or system of equations) is one that has no possible solutions. That is precisely why we call it inconsistent; there is no solution set that can be substituted for its variable or variables that will make the equation (or system) true.
An identity equation has infinite solutions.
Without an equality sign the given terms can't be considered to be an equation and so therefore no solutions are possible.
It will depend on the equation.
None because without an equality sign it is not an equation and so therefore no solutions are possible.
yes
To determine whether a polynomial equation has imaginary solutions, you must first identify what type of equation it is. If it is a quadratic equation, you can use the quadratic formula to solve for the solutions. If the equation is a cubic or higher order polynomial, you can use the Rational Root Theorem to determine if there are any imaginary solutions. The Rational Root Theorem states that if a polynomial equation has rational solutions, they must be a factor of the constant term divided by a factor of the leading coefficient. If there are no rational solutions, then the equation has imaginary solutions. To use the Rational Root Theorem, first list out all the possible rational solutions. Then, plug each possible rational solution into the equation and see if it is a solution. If there are any solutions, then the equation has imaginary solutions. If not, then there are no imaginary solutions.
If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.
It has the following solutions.