College Algebra

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Solve the system of equations using matrices. If system has no solution say its inconsistent.

6x + y = 5
3x - y + z - w = 8
z + w = 2


Solve the system of equations using Cramers Rule if applicable.

4x + 2y = 8/5
5x - 5y = 5

  • College Algebra -

    1.
    Rewrite system in augmented matrix form:
    0 6 1 0 5
    1 3 -1 1 8
    1 0 0 1 2

    Solve by Gaussian elimination.
    With 3 equations and 4 unknowns (w,x,y,z), the solution will be in terms of one of the unknowns and not completely numeric. It could also be inconsistent.

    2.
    Find the determinant of D=
    4 2
    5 -5
    D=4*(-5)-5*2=-30
    Dx (obtained by replacing the x column with the column vector)
    8/5 2
    5 -5
    = (8/5)*(-5) - 5*2
    =-18
    Dy =
    4 8/5
    5 5
    = 4*5 - 5*(8/5)
    = 12
    x=Dx/D=-18/(-30)=3/5
    y=Dy/D=12/(-30)=-2/5
    Check: 4x+2y = 8/5
    5x-5y = 5
    OK

  • College Algebra -

    Solve each system graphically. Be sure to check your solution. If a system has an infinite number of solutions, use set−builder notation to write the solution set. If a system has no solution, state this.
    2x − y = 4,
    5x − y = 13

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