Equations, terminology

Summary

• An equation is a statement formulated as an equality containing one or more variables .
• For example \(2x+1=5\) is an equation containing one variable. Unknowns is another word for variables.
• A value of the variable that makes the equality true is called a solution to the equation. \(x=2\) is the only solution to the equation \(2x+1=5\) .
• A system of equations is a set of simultaneous equations containing one or more variables, for example \(x+y=2\) and \(x-y=0\) is a system of two equations with two variables.
• \(x=1, y=1\) is the only solution to the system \(x+y=2\) and \(x-y=0\) .
• An equation may have
• no solution (e.g. \(x^2=-1\) among the real numbers),
• one solution (e.g. \(2x+1=5\) ),
• \(n\) solutions where \(n\) is a natural number (e.g. \(x^2=1\) has two solutions, \(x=1\) and \(x=-1\) ) or
• an infinite number of solutions (e.g. \(x+y=0\) ).
• An identity is a statement resembling an equation which is true for all possible values of the variable(s) it contains (e.g. \((x+y)(x-y)=x^2-y^2\) ).