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2. Equation solving - Wikipedia

   en.wikipedia.org/wiki/Equation_solving

   For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement. It is also possible to take the variable y to be the unknown, and then the equation is solved by y = x – 1.

3. Algebra - Wikipedia

   en.wikipedia.org/wiki/Algebra

   To do so, the different variables in the equation are understood as coordinates and the values that solve the equation are interpreted as points of a graph. For example, if x {\displaystyle x} is set to zero in the equation y = 0.5 x − 1 {\displaystyle y=0.5x-1} , then y {\displaystyle y} must be −1 for the equation to be true.

4. Elementary algebra - Wikipedia

   en.wikipedia.org/wiki/Elementary_algebra

   Elementary algebra, also known as high school algebra or college algebra, [1] encompasses the basic concepts of algebra. It is often contrasted with arithmetic : arithmetic deals with specified numbers , [ 2 ] whilst algebra introduces variables (quantities without fixed values).

5. Theory of equations - Wikipedia

   en.wikipedia.org/wiki/Theory_of_equations

   Since then algebra has been dramatically enlarged to include many new subareas, and the theory of algebraic equations receives much less attention. Thus, the term "theory of equations" is mainly used in the context of the history of mathematics , to avoid confusion between old and new meanings of "algebra".

6. Algebraic equation - Wikipedia

   en.wikipedia.org/wiki/Algebraic_equation

   In mathematics, an algebraic equation or polynomial equation is an equation of the form =, where P is a polynomial with coefficients in some field, often the field of the rational numbers. For example, x 5 − 3 x + 1 = 0 {\displaystyle x^{5}-3x+1=0} is an algebraic equation with integer coefficients and

7. Consistent and inconsistent equations - Wikipedia

   en.wikipedia.org/wiki/Consistent_and...

   The system + =, + = has exactly one solution: x = 1, y = 2 The nonlinear system + =, + = has the two solutions (x, y) = (1, 0) and (x, y) = (0, 1), while + + =, + + =, + + = has an infinite number of solutions because the third equation is the first equation plus twice the second one and hence contains no independent information; thus any value of z can be chosen and values of x and y can be ...