Algebra: Expressions with Two Variables

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In algebra, an expression is any group of numbers, variables, and/or operators (+, −, ×, ÷, √, and the rest) that represent a value. Here are some examples:

  • 4y + 2
  • x2
  • 15 − 4r

It is also possible for an algebraic expression to have more than one variable, like these:

  • x + y
  • 3m + 4n
  • 2(c − 3x)2

Some algebraic expressions have more than one variable. You may be asked to evaluate or simplify an expression: this just means to perform the operations (add, subtract, multiply, etc.). This can only be done when you are given a value for the variables in the expression. Let’s take a look at an example question:

  • Evaluate the expression x + 5y if x = 4 and y = 3
  • First, replace the values with the given values: x + 5y becomes 4 + 5(3)
  • Then, perform the indicated operations, making sure to follow the order of operations:4 + 5(3) = 4 + 15 = 19

It’s that simple! Substitute the given values, and then perform the operations in the correct order. Now, try some of these practice problems!