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How to Calculate Algebraic Equations

An algebraic equation includes constant numbers and one or more unknown variables. The variables are normally represented by letters, such as X and Y. Both sides of an equation must be equal in value, and that principle will help you calculate an unknown variable in algebraic equations.

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Instructions

- 1
  Solve an equation that has one unknown variable by isolating the unknown variable on one side of the equation's equal sign. In the equation X + 17 = 30, isolate X on one side and keep the equation balanced by subtracting 17 from both sides of the equation. The process to find X for that equation is:
  
  (X + 17) - 17 = 30 - 17
  
  X = 30 - 17
  
  X = 13
  
  The solution procedure for the equation 3X + 5 = 17 is:
  
  (3X + 5) - 5 = 17 - 5
  
  3X = 12
  
  (3X) / 3 = 12 / 3 (with "/" meaning "divided by")
  
  X = 12 / 3
  
  X = 4
- 2
  Solve an equation with the same unknown variable on both sides of the equal sign by isolating the unknown variable on one side of the equal sign. To isolate the unknown variable on one side, keep both sides of the equal by performing the same operations on both sides of the equal sign. For the equation X + 16 = 2X + 11, the process is:
  
  (X + 16) - X = (2X + 11) - X
  
  16 = X + 11
  
  16 -- 11 = (X + 11) - 11
  
  5 = X
  
  For the equation X + 23 = 3X + 45, use this process:
  
  (X + 23) - X = (3X + 45) - X
  
  23 = 2X + 45
  
  23 - 45 = (2X + 45) - 45
  
  -22 = 2X
  
  -22 / 2 = 2X / 2
  
  -11 = X
  
  The coefficient of an unknown variable is the number by which the unknown variable is multiplied. For 2X, the coefficient of X is 2. If the variable has no visible coefficient, in this case X, then the coefficient is 1.
- 3
  Solve equations with two or more different variables by using simultaneous equations. Simultaneous equations are two equations with two unknown variables. They are called "simultaneous" because both must be solved at the same time in order to calculate the unknown variables. For example:
  
  Equation 1 is 2X + Y = 7
  
  Equation 2 is 3X - Y = 8
  
  Add the two equations to cancel out Y:
  
  (2X + Y) + (3X - Y) = 7 + 8
  
  The result is:
  
  2X + 3X = 7 + 8
  
  5X = 15
  
  5X / 5 = 15 / 5
  
  X = 3
  
  If X = 3, then 2(3) + Y = 7
  
  6 + Y = 7
  
  Y = 7 - 6
  
  Y = 1
  
  If this is the correct answer, it should work correctly in Equation 2:
  
  3(3) - 1 = 8
  
  9 - 8 = 8
  
  So the answer is: X = 3, Y = 1
  
  Sometimes it is necessary to multiply one of the equations before you can add or subtract.

Numerology