Download Practice 10

MAT 117
Practice 10
Solve the following systems of linear equations. For practice, use both the substitution and elimination methods.
State “NO SOLUTION” if the system is inconsistent. Answer in fraction form if necessary, no decimal
approximations.
1) 5x – y = -17
2) 6x – y = 0
3) 3x + 4y =1
4) 4x – y = 16
3x + 7y = 5
y = 3x + 1
2x – 3y = -5
5x – 2y = 17
5) 3x – y = 9
6x – 2y = 11
6) 2x – 5y = 10
4x – 10y = 20
7) 8x – 2y = 5
4x + 4y = 5
8) 3x – y = 9
x + 5y = 3
Use any method to solve the following systems of linear equations. State “NO SOLUTION” if the system is
inconsistent. Answer in fraction form if necessary, no decimal approximations.
9)
3x + 2y + z = 10
x – 4y + 2z = -1
4x + y – z = 3
12)
2x – 4y + 6z = 12
x – 2y + 3z = 6
–6x + 12y – 18z = –36
10)
x + 4y + 3z = 8
x + 8y + 6z = 10
2x + 12y + 9z = 18
13)
4x + y = 7
y – 5z = 5
x + 2y – z = -5
11)
3x + 6y + 9z = 14
x + 2y + 3z = 11
2x + 4y + 6z = 13
14)
x + 2z = 1
2x + y + 7z = 6
x + y + 5z = 5
Solutions to Practice 10 (revision 0)
1 
2)  , 2 
3) (-1, 1)
3 
 2 x  10 
6)  x,
 for any real number x
5 

2  4y 

10)  6, y,
 for any real number y
3 

1) (-3, 2)
4) (5, 4)
5) No Solution
3 1
7)  , 
4 2
8) (3, 0)
6  x  2y 

12)  x, y,
 for any real numbers x and y
3


14) (x, 3x + 1, 1 – x) for any real number x
11) No Solution
13) (3, -5, -2)
9) (1, 2, 3)