System of linear equations

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Intros
Lessons
  1. \bullet The solutions to a system of equations are the points of intersection of the graphs.
    \bullet For a system consisting of two linear equations: System of linear equations
    There are 3 cases to consider:
    Graphs of system of linear equations with different number of solutions
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Examples
Lessons
  1. Solving by Elimination
    Solve each linear system algebraically by elimination.
    1. 3x+4y=113x+4y=11
      x4y=7x-4y=-7
    2. 6x1=2y6x-1=2y
      9x+4=5y9x+4=5y
    3. 3(x+2)(y+7)=103(x+2)-(y+7)=-10
      5(x+1)+(y+3)=195(x+1)+(y+3)=19
  2. Solving by Substitution
    Solve each linear system algebraically by substitution.
    1. 6x1y=76x-1y=7
      9x+2y=7-9x+2y=7
    2. 3(x+2)(y+7)=43(x+2)-(y+7)=4
      5(x+1)+4(y+3)=315(x+1)+4(y+3)=31
    3. xy=1x - y = -1
      3x+5y=213x + 5y = 21
Topic Notes
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