# A+ Answers - Gauss Jordan elimination

Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
x - 2y + z = 0
y - 3z = -1
2y + 5z = -2
A. {(-1, -2, 0)}
B. {(-2, -1, 0)}
C. {(-5, -3, 0)}
D. {(-3, 0, 0)}
Question 2 of 40

use Cramer’s Rule to solve the following system.
x + y + z = 0
2x - y + z = -1
-x + 3y - z = -8
A. {(-1, -3, 7)}
B. {(-6, -2, 4)}
C. {(-5, -2, 7)}
D. {(-4, -1, 7)}
Question 3 of 40

use Gauss-Jordan elimination to solve the system.
-x - y - z = 1
4x + 5y = 0
y - 3z = 0
A. {(14, -10, -3)}
B. {(10, -2, -6)}
C. {(15, -12, -4)}
D. {(11, -13, -4)}
Question 4 of 40
2.5/ 2.5 Points
Use Cramer’s Rule to solve the following system.
2x = 3y + 2
5x = 51 - 4y
A. {(8, 2)}
B. {(3, -4)}
C. {(2, 5)}
D. {(7, 4)}
Question 5 of 40

use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
w - 2x - y - 3z = -9
w + x - y = 0
3w + 4x + z = 6
2x - 2y + z = 3
A. {(-1, 2, 1, 1)}
B. {(-2, 2, 0, 1)}
C. {(0, 1, 1, 3)}
D. {(-1, 2, 1, 1)}
Question 6 of 40

Use Cramer’s Rule to solve the following system.

x + y = 7
x - y = 3
A. {(7, 2)}
B. {(8, -2)}
C. {(5, 2)}
D. {(9, 3)}
Question 7 of 40

Use Cramer’s Rule to solve the following system.
3x - 4y = 4
2x + 2y = 12
A. {(3, 1)}
B. {(4, 2)}
C. {(5, 1)}
D. {(2, 1)}
Question 8 of 40
2.5/ 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
x + y + z = 4
x - y - z = 0
x - y + z = 2
A. {(3, 1, 0)}
B. {(2, 1, 1)}
C. {(4, 2, 1)}
D. {(2, 1, 0)}
Question 9 of 40

Find values for x, y, and z so that the following matrices are equal.
2x
z               y + 7
4                            =                           -10
6               13
4
A. x = -7; y = 6; z = 2
B. x = 5; y = -6; z = 2
C. x = -3; y = 4; z = 6
D. x = -5; y = 6; z = 6
Question 10 of 40
2.5/ 2.5 Points
Use Cramer’s Rule to solve the following system.
4x - 5y - 6z = -1
x - 2y - 5z = -12
2x - y = 7
A. {(2, -3, 4)}
B. {(5, -7, 4)}
C. {(3, -3, 3)}
D. {(1, -3, 5)}
Question 11 of 40
2.5/ 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
x + y - z = -2
2x - y + z = 5
-x + 2y + 2z = 1
A. {(0, -1, -2)}
B. {(2, 0, 2)}
C. {(1, -1, 2)}
D. {(4, -1, 3)}
Question 12 of 40

Use Cramer’s Rule to solve the following system.

12x + 3y = 15
2x - 3y = 13
A. {(2, -3)}
B. {(1, 3)}
C. {(3, -5)}
D. {(1, -7)}
Question 13 of 40
2.5/ 2.5 Points
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
8x + 5y + 11z = 30
-x - 4y + 2z = 3
2x - y + 5z = 12
A. {(3 - 3t, 2 + t, t)}
B. {(6 - 3t, 2 + t, t)}
C. {(5 - 2t, -2 + t, t)}
D. {(2 - 1t, -4 + t, t)}
Question 14 of 40
2.5/ 2.5 Points
Use Gaussian elimination to find the complete solution to each system.
2x + 3y - 5z = 15
x + 2y - z = 4
A. {(6t + 28, -7t - 6, t)}
B. {(7t + 18, -3t - 7, t)}
C. {(7t + 19, -1t - 9, t)}
D. {(4t + 29, -3t - 2, t)}
Question 15 of 40
2.5/ 2.5 Points
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
5x + 8y - 6z = 14
3x + 4y - 2z = 8
x + 2y - 2z = 3
A. {(-4t + 2, 2t + 1/2, t)}
B. {(-3t + 1, 5t + 1/3, t)}
C. {(2t + -2, t + 1/2, t)}
D. {(-2t + 2, 2t + 1/2, t)}
Question 16 of 40

Solve the system using the inverse that is given for the coefficient matrix.
2x + 6y + 6z = 8
2x + 7y + 6z =10
2x + 7y + 7z = 9
The inverse of:
2
2
2               6
7
7               6
6
7
is
7/2
-1
0               0
1
-1             -3
0
1
A. {(1, 2, -1)}
B. {(2, 1, -1)}
C. {(1, 2, 0)}
D. {(1, 3, -1)}
Question 17 of 40
2.5/ 2.5 Points
Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists.
2w + x - y = 3
w - 3x + 2y = -4
3w + x - 3y + z = 1
w + 2x - 4y - z = -2
A. {(1, 3, 2, 1)}
B. {(1, 4, 3, -1)}
C. {(1, 5, 1, 1)}
D. {(-1, 2, -2, 1)}
Question 18 of 40
2.5/ 2.5 Points
Solve the following system of equations using matrices. Use Gaussian elimination with back substitution or Gauss-Jordan elimination.
x + 2y = z - 1
x = 4 + y - z
x + y - 3z = -2
A. {(3, -1, 0)}
B. {(2, -1, 0)}
C. {(3, -2, 1)}
D. {(2, -1, 1)}
Question 19 of 40
2.5/ 2.5 Points
Use Cramer’s Rule to solve the following system.
x + 2y + 2z = 5
2x + 4y + 7z = 19
-2x - 5y - 2z = 8
A. {(33, -11, 4)}
B. {(13, 12, -3)}
C. {(23, -12, 3)}
D. {(13, -14, 3)}
Question 20 of 40

Use Cramer’s Rule to solve the following system.

4x - 5y = 17
2x + 3y = 3
A. {(3, -1)}
B. {(2, -1)}
C. {(3, -7)}
D. {(2, 0)}
Part 2 of 2 - Lesson 7 Questions   20.0/ 50.0 Points
Question 21 of 40

Find the vertex, focus, and directrix of each parabola with the given equation.
(y + 1)2 = -8x
A. Vertex: (0, -1); focus: (-2, -1); directrix: x = 2
B. Vertex: (0, -1); focus: (-3, -1); directrix: x = 3
C. Vertex: (0, -1); focus: (2, -1); directrix: x = 1
D. Vertex: (0, -3); focus: (-2, -1); directrix: x = 5
Question 22 of 40
2.5/ 2.5 Points
Convert each equation to standard form by completing the square on x and y.
9x2 + 16y2 - 18x + 64y - 71 = 0
A. (x - 1)2/9 + (y + 2)2/18 = 1
B. (x - 1)2/18 + (y + 2)2/71 = 1
C. (x - 1)2/16 + (y + 2)2/9 = 1
D. (x - 1)2/64 + (y + 2)2/9 = 1
Question 23 of 40
2.5/ 2.5 Points
Find the focus and directrix of the parabola with the given equation.
8x2 + 4y = 0
A. Focus: (0, -1/4); directrix: y = 1/4
B. Focus: (0, -1/6); directrix: y = 1/6
C. Focus: (0, -1/8); directrix: y = 1/8
D. Focus: (0, -1/2); directrix: y = 1/2
Question 24 of 40

Locate the foci and find the equations of the asymptotes.

x2/100 - y2/64 = 1
A. Foci: ({= ±2√21, 0); asymptotes: y = ±2/5x
B. Foci: ({= ±2√31, 0); asymptotes: y = ±4/7x
C. Foci: ({= ±2√41, 0); asymptotes: y = ±4/7x
D. Foci: ({= ±2√41, 0); asymptotes: y = ±4/5x
Question 25 of 40

Find the standard form of the equation of each hyperbola satisfying the given conditions.
Foci: (0, -3), (0, 3)
Vertices: (0, -1), (0, 1)
A. y2 - x2/4 = 0
B. y2 - x2/8 = 1
C. y2 - x2/3 = 1
D. y2 - x2/2 = 0
Question 26 of 40
2.5/ 2.5 Points
Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola.
x2 - 2x - 4y + 9 = 0
A. (x - 4)2 = 4(y - 2); vertex: (1, 4); focus: (1, 3) ; directrix: y = 1
B. (x - 2)2 = 4(y - 3); vertex: (1, 2); focus: (1, 3) ; directrix: y = 3
C. (x - 1)2 = 4(y - 2); vertex: (1, 2); focus: (1, 3) ; directrix: y = 1
D. (x - 1)2 = 2(y - 2); vertex: (1, 3); focus: (1, 2) ; directrix: y = 5
Question 27 of 40
2.5/ 2.5 Points
Find the vertices and locate the foci of each hyperbola with the given equation.
x2/4 - y2/1 =1
A.
Vertices at (2, 0) and (-2, 0); foci at (√5, 0) and (-√5, 0)
B.
Vertices at (3, 0) and (-3 0); foci at (12, 0) and (-12, 0)
C. Vertices at (4, 0) and (-4, 0); foci at (16, 0) and (-16, 0)
D. Vertices at (5, 0) and (-5, 0); foci at (11, 0) and (-11, 0)
Question 28 of 40
2.5/ 2.5 Points
Convert each equation to standard form by completing the square on x and y.
9x2 + 25y2 - 36x + 50y - 164 = 0
A. (x - 2)2/25 + (y + 1)2/9 = 1
B. (x - 2)2/24 + (y + 1)2/36 = 1
C. (x - 2)2/35 + (y + 1)2/25 = 1
D. (x - 2)2/22 + (y + 1)2/50 = 1
Question 29 of 40

Convert each equation to standard form by completing the square on x and y.
4x2 + y2 + 16x - 6y - 39 = 0
A. (x + 2)2/4 + (y - 3)2/39 = 1
B. (x + 2)2/39 + (y - 4)2/64 = 1
C. (x + 2)2/16 + (y - 3)2/64 = 1
D. (x + 2)2/6 + (y - 3)2/4 = 1
Question 30 of 40
2.5/ 2.5 Points
Locate the foci of the ellipse of the following equation.

7x2 = 35 - 5y2
A. Foci at (0, -√2) and (0, √2)
B. Foci at (0, -√1) and (0, √1)
C. Foci at (0, -√7) and (0, √7)
D. Foci at (0, -√5) and (0, √5)
Question 31 of 40
2.5/ 2.5 Points
Find the vertex, focus, and directrix of each parabola with the given equation.
(x + 1)2 = -8(y + 1)
A. Vertex: (-1, -2); focus: (-1, -2); directrix: y = 1
B. Vertex: (-1, -1); focus: (-1, -3); directrix: y = 1
C. Vertex: (-3, -1); focus: (-2, -3); directrix: y = 1
D. Vertex: (-4, -1); focus: (-2, -3); directrix: y = 1
Question 32 of 40

Find the vertices and locate the foci of each hyperbola with the given equation.
y2/4 - x2/1 = 1
A. Vertices at (0, 5) and (0, -5); foci at (0, 14) and (0, -14)
B. Vertices at (0, 6) and (0, -6); foci at (0, 13) and (0, -13)
C.
Vertices at (0, 2) and (0, -2); foci at (0, √5) and (0, -√5)
D. Vertices at (0, 1) and (0, -1); foci at (0, 12) and (0, -12)
Question 33 of 40
2.5/ 2.5 Points
Find the vertex, focus, and directrix of each parabola with the given equation.
(x - 2)2 = 8(y - 1)
A. Vertex: (3, 1); focus: (1, 3); directrix: y = -1
B. Vertex: (2, 1); focus: (2, 3); directrix: y = -1
C. Vertex: (1, 1); focus: (2, 4); directrix: y = -1
D. Vertex: (2, 3); focus: (4, 3); directrix: y = -1
Question 34 of 40

Find the standard form of the equation of the ellipse satisfying the given conditions.
Endpoints of major axis: (7, 9) and (7, 3)
Endpoints of minor axis: (5, 6) and (9, 6)
A. (x - 7)2/6 + (y - 6)2/7 = 1
B. (x - 7)2/5 + (y - 6)2/6 = 1
C. (x - 7)2/4 + (y - 6)2/9 = 1
D. (x - 5)2/4 + (y - 4)2/9 = 1
Question 35 of 40

Find the standard form of the equation of the following ellipse satisfying the given conditions.
Foci: (0, -4), (0, 4)
Vertices: (0, -7), (0, 7)
A. x2/43 + y2/28 = 1
B. x2/33 + y2/49 = 1
C. x2/53 + y2/21 = 1
D. x2/13 + y2/39 = 1
Question 36 of 40

Find the focus and directrix of each parabola with the given equation.
x2 = -4y
A. Focus: (0, -1), directrix: y = 1
B. Focus: (0, -2), directrix: y = 1
C. Focus: (0, -4), directrix: y = 1
D. Focus: (0, -1), directrix: y = 2
Question 37 of 40

Convert each equation to standard form by completing the square on x or y. Then ﬁnd the vertex, focus, and directrix of the parabola.
y2 - 2y + 12x - 35 = 0
A. (y - 2)2 = -10(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 9
B. (y - 1)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 6
C. (y - 5)2 = -14(x - 3); vertex: (2, 1); focus: (0, 1); directrix: x = 6
D. (y - 2)2 = -12(x - 3); vertex: (3, 1); focus: (0, 1); directrix: x = 8
Question 38 of 40

Find the standard form of the equation of the following ellipse satisfying the given conditions.
Foci: (-5, 0), (5, 0)
Vertices: (-8, 0), (8, 0)
A. x2/49 + y2/ 25 = 1
B. x2/64 + y2/39 = 1
C. x2/56 + y2/29 = 1
D. x2/36 + y2/27 = 1
Question 39 of 40
Find the standard form of the equation of the following ellipse satisfying the given conditions.
Foci: (-2, 0), (2, 0)
Y-intercepts: -3 and 3
A. x2/23 + y2/6 = 1
B. x2/24 + y2/2 = 1
C. x2/13 + y2/9 = 1
D. x2/28 + y2/19 = 1
Question 40 of 40

Find the standard form of the equation of each hyperbola satisfying the given conditions.
Endpoints of transverse axis: (0, -6), (0, 6)
Asymptote: y = 2x
A. y2/6 - x2/9 = 1
B. y2/36 - x2/9 = 1
C. y2/37 - x2/27 = 1
D. y2/9 - x2/6 = 1