The collection of letters representing numbers
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The letters in most algebraic equations mostly represent the value of the number or often at times the gradient.
Its called Simultaneous Equations
Algebraic equations, trigenometric equations, linear equations, geometric equations, partial differential equations, differential equations, integrals to name a few.
When you combine to equations and you find if they are equal or not
Algebraic expressions are the written relations of or between variables. For example, x2, 1/x, and x + y + z are all algebraic expressions. Algebraic equations are simply algebraic expressions that equate to something. For example, x2 = 4, 1/x = y, and x + y + z = 42 are all algebraic equations. In general, one differentiates algebraic expressions from exponential, trigonometric, hyperbolic, and logarithmic expressions by requiring algebraic expressions to be confined to polynomial expressions. I've added a link regarding polynomials below.