Classification of equations

Summary

• The expression \(a+bx\) is said to be a linear expression in the \(x\) -variable If \(a,b\) are constants and \(x\) is a variable.
• An equation is said to be linear if all sides of the equation are linear in the variable.
• The expression \(ax^2+bx+c\) is said to be a quadratic expression in the \(x\) -variable if \(a,b,c\) are constants, \(a≠0\) and \(x\) is a variable.
• The equation \(ax^2+bx+c=0\) is called a quadratic equation if \(a, b, c\) are constants, \(a≠0\) and \(x\) is a variable.
• The expression \(x^2+px+q\) is said to be a reduced quadratic expression in the \(x\) -variable If \(p,q\) are constants and \(x\) is a variable.
• The equation \(x^2+px+q=0\) is called a reduced quadratic equation if \(p,q\) are constants and \(x\) is a variable.
• If \(a,b, c\) are constants and \(x, y\) are variables then the expression \(a+bx+cy\) is said to be a linear expression in all the variables . This definition may be extended to an arbitrary number of variables and constants.
• An equation or a system of equations is said to be linear if all sides of the equation(s) are linear in all the variables.
• Two equations or two systems of equations are said to be equivalent if they have the same solutions. For example, \(2x+1=5\) is equivalent to \(2x=4\) .