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.
If the solution contains one variable which has not been fixed then there are infinitely many solution.
There are infinitely many solutions. One linear equation in two variables cannot be solved to give a single answer.
That looks like a linear equation (no quadratic or higher terms), so you can expect it to have a single solution. However, actually solving the equation is not difficult; do it, to confirm this.
If the discriminant of a quadratic equation is less then 0 then it will have no real solutions.
A linear equation in one variable has one solution. An equation of another kind may have none, one, or more - including infinitely many - solutions.
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As many solutions as there are points in the domain.
Either an infinite number or none.
Linear equations with one, zero, or infinite solutions. Fill in the blanks to form a linear equation with infinitely many solutions.
Inequalities tend to have infinitely many solutions.
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-- 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.
A linear equation is that of a straight line. Any one of the infinitely many points on the line will be solutions. If the equation is in terms of the variables x and y, just pick any two values of x, solve for y and the results will be the coordinates of two 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.
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.