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Use Cramer's rule to solve the system. 6) 6x + 6y = -12

Question : Use Cramer's rule to solve the system. 6) 6x + 6y = -12 : 2151861

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Evaluate the determinant.

1)

A) 34

B) -44

C) 62

D) -34

2)

A) 29

B) 19

C) -43

D) -29

3)

A) 1

B) -1

C) -5

D) 5

4)

A) 0

B) -2

C) 2

D) 26/5

5)

A) -235/792

B) -25/528

C) 45/176

D) 5/1056

Use Cramer's rule to solve the system.

6) 6x + 6y = -12

4x + y = -17

A) {(-3, -5)}

B) {(3, -5)}

C) {(-5, -3)}

D) {(-5, 3)}

7) 2x + 2y = 16

-2x + 4y = -4

A) {(2, 6)}

B) {(-2, 6)}

C) {(6, -2)}

D) {(6, 2)}

8) 2x + 3y = 33

3x - 2y = -9

A) {(-3, -9)}

B) {(-9, 3)}

C) {(3, 9)}

D) {(9, 3)}

9) 7x + 8y = 4

2x + 3y = 2

A) {(- 4/5, 6/5)}

B) {(- 5/4, 5/6)}

C) {(6/5, - 4/5)}

D) {(28/37, 22/37)}

10) 4x = -4y + 8

5x = -y - 10

A) {(-3, 5)}

B) {(5, -3)}

C) {(-3, -5)}

D) {(-5, -3)}

11) 4x = 18 + 2y

4y = 34 - 2x

A) {(5, 7)}

B) {(-5, 7)}

C) {(7, 5)}

D) {(7, -5)}

Evaluate the determinant.

12)

A) 133

B) 623

C) -128

D) -133

13)

A) -3

B) -7

C) 7

D) 3

14)

A) 1

B) 92

C) 0

D) -20

15)

A) -144

B) 220

C) 6

D) -6

Solve the problem.

16) The area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is

,

where the symbol ± indicates that the appropriate sign should be chosen to yield a positive area. Use this formula to find the area of a triangle whose vertices are (10, 2), (4, -9), and (-5, -4).

A) 129

B) 23/2

C) 129/2

D) 23

17) Determinants are used to show that three points lie on the same line (are collinear). If

 = 0,

then the points (x1, y1), (x2, y2), and (x3, y3) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points (-2, -1), (0,3), and (-4, -5) collinear?

A) No

B) Yes

18) Determinants are used to show that three points lie on the same line (are collinear). If

 = 0,

then the points (x1, y1), (x2, y2), and (x3, y3) are collinear. If the determinant does not equal 0, then the points are not collinear. Are the points (9, -4), (0,1), and(36, -17) collinear?

A) Yes

B) No

19) The equation of a line passing through two distinct points (x1, y1), (x2, y2) is given by

 Use the determinant to write an equation for the line passing through (6, 8) and (-3, -6). Express the line's equation in standard form.

A) 8x - 3y - 36 = 0

B) -6x + 6y - 24 = 0

C) 14x - 9y - 12 = 0

D) -14x + 9y - 12 = 0

Use Cramer's rule to solve the system.

20) 9x + 6y - z = 103

x + 4y - 4z = 17

-2x + y + z = -12

A) {(4, 2, 4)}

B) {(9, -4, -2)}

C) {(10, 2, 2)}

D) {(9, 4, 2)}

21) 8x - 9y - 2z = -43

-2x + 7y - 7z = -14

-3x - 9y - 5z = -147

A) {(8, 7, 9)}

B) {(7, -9, -9)}

C) {(9, 9, 9)}

D) {(7, 9, 9)}

22) 4x - 7z = 13

5x + 6y + 3z = 34

-4x - 5y = -25

A) {(1, 1, 1)}

B) {(6, -1, 1)}

C) {(5, -1, -1)}

D) {(5, 1, 1)}

23) 4x + 5y - z = 66

x - 3y + 5z = -8

5x + y + z = 48

A) {(7, 1, 7)}

B) {(8, 7, 1)}

C) {(9, 5, 1)}

D) {(8, -7, -1)}

24) 3x - 2y + 2z = 9

2y - 3z = -6

2x + 2z = 18

A) {(6, 6, 6)}

B) {(4, 4, 6)}

C) {(3, 6, 6)}

D) {(3, -6, -6)}

Use Cramer's rule to determine if the system is inconsistent system or contains dependent equations.

25) 4x + y = 11

8x + 2y = 22

A) system contains dependent equations

B) system is inconsistent

26) 3x – 5y = -7

6x – 10y = -9

A) system is inconsistent

B) system contains dependent equations

27) 9x + y = 20

9x + y = 65

A) system is inconsistent

B) system contains dependent equations

28) 4x - y + 2z = 1

3x + 5y - z = 0

-6x - 10y + 2z = 0

A) system is inconsistent

B) system contains dependent equations

29) x + z = 1

2x - 2y = -2

y + z = 4

A) system is inconsistent

B) system contains dependent equations

Evaluate the determinant.

30)

A) -351

B) -63

C) -9

D) 351

31)

A) 1980

B) 0

C) -27

D) -30

32)

A) -13

B) 6

C) -30

D) -46

Solution
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