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
