System of Linear Equations

System of Linear Equations

1. A System of Equations is when we have two or more equations working together.

2. Example:

   • It's a race! You can run 0.2 km every minute. The Horse can run 0.5 km every minute. But it takes 6 minutes to saddle the horse. How far can you get before the horse catches you? Two equations (d=distance in km, t=time in minutes): You: d= 0.2t The horse: d=0.5(t-6)

3. Solving System of Linear Equation

   • Substitution Method
     • 1.Write one of the equations so it is in the style "variable = ..."
     • 2.Replace (i.e. substitute) that variable in the other equation(s)
     • 3.Solve the other equation(s)
   • Elimination Method
     • "Eliminate" means to remove: this method works by removing variables until there is just one left.
       • We can multiply an equation by a constant (except zero)
       • We can add (or subtract) an equation on to another equation

4. Solutions

5. Substitution is often easier for small cases (like 2 equations, or sometimes 3 equations) Elimination is easier for larger cases

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