Posted by **coried** on Sunday, September 13, 2009 at 5:32pm.

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 -
**MathMate**, Sunday, September 13, 2009 at 9:16pm
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 -
**sherry**, Monday, November 14, 2011 at 10:18pm
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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