Examples of extraneous solution in the following topics:

 However, squaring both sides can introduce extraneous solutions (i.e., false answers), so it is important to check the answers after solving.
 If no answer checks out, then the solution is "no solution."
 Therefore, $x=17$ is a valid solution to the equation $\sqrt{6x2}3=7$.
 This means that $10.2$ is an extraneous solution.
 Because it is the only answer we found, the answer to this problem is "no solution."

 Some linear systems may not have a solution, while others may have an
infinite number of solutions.
 Even so, this does not guarantee a unique solution.
 A solution to the system above is given by
 An inconsistent system has no solution.
 A dependent system
has infinitely many solutions.

 Equations in two variables have not one solution but a series of solutions that will satisfy the equation for both variables.
 Each solution is an ordered pair and can be written in the form $(x, y)$.
 For example, $(1, 2)$ is a solution to the equation.
 Another solution is $(30, 60)$, because $(60) = 2(30)$.
 Therefore, the solution is $(3, 5)$.

 In our study of linear equations in two variables, we observed that all
the solutions to an equation—and only those solutions—
were located on the graph of that equation.
 The resulting ordered pair will be one solution to the equation.
 So, let's substitute $x = 0 $ to find one solution:
 Graph showing all possible solutions of the given inequality.
 The solutions lie in the shaded region, including the boundary line.

 Independent systems have a single solution.
 Dependent systems have an infinite number of solutions.
 Inconsistent systems have no solution.
 An infinite number of
solutions can result from several situations.
 The three planes could be
the same, so that a solution to one equation will be the solution to
the other two equations.

 Two properties of a linear system are consistency (are there solutions?
 A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied.
 A solution to the system above is given by
 A linear system is consistent if it has a solution, and inconsistent otherwise.
 Note that any two of these equations have a common solution.

 For linear equations in two variables, inconsistent systems have no solution, while dependent systems have infinitely many solutions.
 An independent system of equations has exactly one solution $(x,y)$.
 An inconsistent system has no solution, and a dependent system has an infinite number of solutions.
 Note that there are an infinite number of solutions to a dependent system, and these solutions fall on the shared line.
 A
linear system is consistent if it has a solution, and inconsistent
otherwise.

 To find solutions for the group of inequalities, observe where the area of all of the inequalities overlap.
 These overlaps of the shaded regions indicate all solutions (ordered pairs) to the system.
 This also means that if there are inequalities that don't overlap, then there is no solution to the system.
 There are no solutions above the line.
 The origin is a solution to the system, but the point $(3,0)$ is not.

 In an equation with one variable, the variable has a solution, or value, that makes the equation true.
 The values of the variables that make an equation true are called the solutions of the equation.
 Thus, we can easily check whether a number is a genuine solution to a given equation.
 For example, let's examine whether $x=3$ is a solution to the equation $2x + 31 = 37$.
 Therefore, we can conclude that $x = 3$ is, in fact, a solution to the equation $2x+31=37$.

 Note that the expression x > 12 has infinitely many solutions.
 Some solutions are: 13, 15, 90, 12.1, 16.3, and 102.51.
 A linear equation, we know, may have exactly one solution, infinitely many solutions, or no solution.
 Speculate on the number of solutions of a linear inequality.
 A linear inequality may have infinitely many solutions or no solutions.