Multiple Choice Answers

1. Solve the linear system of equations
x-3y= -6
A unique solution 6,4
B unique solution 6,-1
C infinitely many solutions t, 8t+7
D no solution

2. Solve the linear system of equations
2x-6y=7
5x+2y=10
A unique solution 8,3
B unique solution 37/17, -15/34
C infinitely many solutions t,6t+1
D no solution

3. Solve the linear system of equations
x+16y=9
1/4x+4y=8
A unique solution 9,4
B unique solution 2,-4
C infinitely many solutions t, 8t+9
D No solution

4. Solve the linear system of equations
3x-2y=7
9x-6y=14
A unique solution 6,-4
B unique solution 8,5
C infinitely many solutions t,8t+5
D no solution

5. Solve the linear system of equations
X+3y=9
3x-y=7
A one and only one solution 3,2
B one and only one solution 3,4
C one and only one solution 4,2
D infinitely many solutions 9-3k,k
E no solution

6. Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.
2x-5y=10
4x-10y= 20
A one and only one solution 0,-2
B one and only one solution 5,0
C one and only one solution 15/2, 1
D infinitely many solutions 5/2k+5,k
E no solution
7. solve the linear system of equations
7/4x-5/2y=2
1/4x+7/2y=8
A unique solution 7,-4
B unique solution 4,2
C infinitely many solutions t,6t+1
D no solution

8. Solve the linear system of equations
9x-7y=63
45x-35y=18
A unique solution 5,-4
B unique solution 3,4
C infinitely many solutions t,8t+1
D no solution

9. A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are nonparallel.
A true
B false

10. Solve the linear system of equations
6x-7y=20
3x+5y=-7
A unique solution 1,-2
B unique solution -9,3
C infinitely many solutions t,4t+5
D no solution

11. Indicate whether the matrix is in row-reduced form
1 0 l7l
0 1 l5l
A the matrix is not in row- reduced form
B the matrix is in row reduced form

12. Indicate whether the matrix is in row-reduced form

1 0 1 l9l
0 1 0 l8l
0 0 -1 l6l
A the matrix is not in row- reduced form
B the matrix is in row reduced form
13. Indicate whether the matrix is in row-reduced form
1 0 l-12l
0 1 l 2 l
0 0 l 0 l
A the matrix is not in row- reduced form
B the matrix is in row reduced form  if we discard last equation.

14. Indicate whether the matrix is in row-reduced form
1 0 0 l-1l
0 1 1 l-2l
0 0 2 l-3l

A the matrix is not in row- reduced form
B the matrix is in row reduced form

15. Indicate whether the matrix is in row-reduced form
1 0 0 l9l
0 1 0 l6l
0 0 0 l2l
0 0 1 l8l

A the matrix is not in row- reduced form
B the matrix is in row reduced form
Not so sure about this.
16. Solve the system of linear equations using the Gauss-Jordan elimination method.
x-2y=8
3x+4y=4
A (0,2)
B (8,2)
C (4,-6)
D (-2,4)
E (4,-2)

17. Solve the system of linear equations using the Gauss-Jordan elimination method.
3x+2y=14
x-4y=-14
A (2,-14)
B (4,-14)
C (2,4)
D (2,16)
E (4, -14)

18. Solve the system of linear equations using the Gauss-Jordan elimination method.
7x +5y=32
-3x+y=-20
A (7,-3)
B (6,-2)
C (2,-6)
D (-6,2)
E (-7,-2)

19. Solve the system of linear equations using the Gauss-Jordan elimination method.
3x+3y+ z=22
X + z=6
4y-3z=8

A) ( 4, –14, –8 )
B) ( –19, 4, 8 )
C) ( 8, –14, –4 )
D) ( 14, 4, 8 )
E) ( 14, –4, –8 )

20. Solve the system of linear equations, using the Gauss-Jordan elimination method.
2x+5y-2z=14
5x-6y+2z=0
4x- y+3z=-7
A x=2,y=6,z=5
B x=2,y=5,z=-5
C x=2,y=0,z=5
D x=2,y=0,z=-5
E x=5, y=0,z=-2