MAT 117 - Arizona State University



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 6) 2x – 5y = 10 7) 8x – 2y = 5 8) 3x – y = 9

6x – 2y = 11 4x – 10y = 20 4x + 4y = 5 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 12) 2x – 4y + 6z = 12

x – 4y + 2z = -1 x – 2y + 3z = 6

4x + y – z = 3 –6x + 12y – 18z = –36

10) x + 4y + 3z = 8 13) 4x + y = 7

x + 8y + 6z = 10 y – 5z = 5

2x + 12y + 9z = 18 x + 2y – z = -5

11) 3x + 6y + 9z = 14 14) x + 2z = 1

x + 2y + 3z = 11 2x + y + 7z = 6

2x + 4y + 6z = 13 x + y + 5z = 5

Solutions to Practice 10 (revision 0)

1) (-3, 2) 2) [pic] 3) (-1, 1) 4) (5, 4) 5) No Solution

6) [pic]for any real number x 7) [pic] 8) (3, 0) 9) (1, 2, 3)

10) [pic] for any real number y 11) No Solution

12) [pic] for any real numbers x and y 13) (3, -5, -2)

14) (x, 3x + 1, 1 – x) for any real number x

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