Question

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

Answer 1

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

Answer 2

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