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How to Solve Systems of Equations Activity

A system of equations generally consists of two expressions, each containing two variables. They can be used to model systems that are present in everyday life, such as supply and demand. The solution to a system of equations is the point at which the two lines intersect. At this point, the values of x and y are valid for both expressions. A system can be solved graphically or mathematically. An activity can be used to teach students in a class how to solve systems mathematically.

Instructions

- 1
  Identify the two variables to be solved for. For example, if the equations are 3x+2y=6 and 4y=2x+3, then the two variables are "x" and "y".
- 2
  Manipulate one of the equations to the form y=mx+b. The first equation in the example will be y=3-1.5x. The second will be y=.75+.5x.
- 3
  Replace the "y" in the equation not manipulated in step 2 with the value that was found for "y" in step 2. In this example, it would be 12-6x=2x+3 or 3x+1.5+x=6 depending on which equation you chose.
- 4
  Simplify the equation from step 3 by combining like terms. This will yield 9-8x=0 or 4.5-4x=0. Notice that these equations are the same.
- 5
  Solve for "x." This yields x = 9/8.
- 6
  Plug in the value of "x" to determine the value of "y." Use either equation. This yields 4y = 2(9/8)+3. Or, y = 21/16.
- 7
  Plug the "x" and "y" values into the equation not used in step 6 to check your work. This yields 3(9/8)+2(21/16) = 6, or 6 = 6. Therefore, the solution is correct.

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