System of linear equations

System of linear equations

Lessons

  • Introduction
    \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

  • 1.
    Solving by Elimination
    Solve each linear system algebraically by elimination.
    a)
    3x+4y=113x+4y=11
    x4y=7x-4y=-7

    b)
    6x1=2y6x-1=2y
    9x+4=5y9x+4=5y

    c)
    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.
    a)
    6x1y=76x-1y=7
    9x+2y=7-9x+2y=7

    b)
    3(x+2)(y+7)=43(x+2)-(y+7)=4
    5(x+1)+4(y+3)=315(x+1)+4(y+3)=31

    c)
    xy=1x - y = -1
    3x+5y=213x + 5y = 21