How to Solve Systems of Equations

Step-by-Step Guide

1. 1

   Step 1: Write one equation above the other.

   Solving a system of equations by subtraction is ideal when you see that both equations have one variable with the same coefficient with the same charge.
   
   For example, if both equations have the variable positive 2x, you should use the subtraction method to find the value of both variables.
   
   Write one equation above the other by matching up the x and y variables and the whole numbers.
   
   Write the subtraction sign outside the quantity of the second system of equations.
   
   Ex:
   If your two equations are 2x + 4y = 8 and 2x + 2y = 2, then you should write the first equation over the second, with the subtraction sign outside the quantity of the second system, showing that you'll be subtracting each of the terms in that equation. 2x + 4y = 8
   -(2x + 2y = 2)
2. 2

   Step 2: Subtract like terms.

   Now that you've lined up the two equations, all you have to do is subtract the like terms.
   
   You can take it one term at a time: 2x
   - 2x = 0 4y
   - 2y = 2y 8
   - 2 = 6 2x + 4y = 8
   -(2x + 2y = 2) = 0 + 2y = 6 , Once you've eliminated one of the variables by getting a term of 0 when you subtract variables with the same coefficient, you should just solve for the remaining variable by solving a regular equation.
   
   You can remove the 0 from the equation since it won't change its value. 2y = 6 Divide 2y and 6 by 2 to get y = 3 , Now that you know that y = 3, you just have to plug it in to one of the original equations to solve for x.
   
   It doesn't matter which one you choose because the answer will be the same.
   
   If one of the equations looks more complicated than the other, just plug it into the easier equation.
   
   Plug y = 3 into the equation 2x + 2y = 2 and solve for x. 2x + 2(3) = 2 2x + 6 = 2 2x =
   -4 x =
   - 2 You have solved the system of equations by subtraction. (x, y) = (-2, 3) , To make sure that you solved the system of equations correctly, you can just plug in your two answers to both equations to make sure that they work both times.
   
   Here's how to do it:
   Plug (-2, 3) in for (x, y) in the equation 2x + 4y =
   8. 2(-2) + 4(3) = 8
   -4 + 12 = 8 8 = 8 Plug (-2, 3) in for (x, y) in the equation 2x + 2y =
   2. 2(-2) + 2(3) = 2
   -4 + 6 = 2 2 = 2
3. 3

   Step 3: Solve for the remaining term.

4. 4

   Step 4: Plug the term back into one of the equations to find the value of the first term.

5. 5

   Step 5: Check your answer.

Detailed Guide

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