near sys- 11. In each part, solve the linear system, if possible, and use the result to determine whether the lines represented by the equa- tions in the system have zero, one, or infinitely many points of intersection. If there is a single point of intersection, give its coordinates, and if there are infinitely many, find parametric equations for them. a. 3x - 2y = 4 c. x-2y = 0 b. 2x - 4y = 1 4x-8y = 2 6x - 4y = 9 x - 4y = 8
near sys- 11. In each part, solve the linear system, if possible, and use the result to determine whether the lines represented by the equa- tions in the system have zero, one, or infinitely many points of intersection. If there is a single point of intersection, give its coordinates, and if there are infinitely many, find parametric equations for them. a. 3x - 2y = 4 c. x-2y = 0 b. 2x - 4y = 1 4x-8y = 2 6x - 4y = 9 x - 4y = 8
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
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Question 7: A,b,c please
Q11: a,b,c please
Q15: a,b please
On paper please.
![al linear
ear sys-
s in the
mented
e lin-
aus 1.1 Introduction to Systems of Linear Equations 9
11. In each part, solve the linear system, if possible, and use the
result to determine whether the lines represented by the equa-
tions in the system have zero, one, or infinitely many points of
intersection. If there is a single point of intersection, give its
coordinates, and if there are infinitely many, find parametric
equations for them.
a. 3x - 2y = 4
6x - 4y = 9
b. 2x - 4y = 1
4x-8y = 2
c. x-2y = 0
x - 4y = 8
12. Under what conditions on a and b will the linear system have
no solutions, one solution, infinitely many solutions?
2x - 3y = a
4x - 6y= b
In each part of Exercises 13-14, use parametric equations to describe
the solution set of the linear equation.
13. a. 7x - 5y = 3
b. 3x₁5x₂ + 4x3 = 7
c. -8x₁ + 2x₂5x3 + 6x4 = 1
d. 3v8w + 2xy + 4z = 0
b. x₁ + 3x₂ - 12x3 = 3
c. 4x₁ + 2x₂ + 3x3 + x4 = 20
d. v+w+x - 5y +7z=0
In Exercises 15-16, each linear system has infinitely many solutions.
Use parametric equations to describe its solution set.
15. a. 2x-3y = 1
6x9y = 3
x3 = -4
b. x₁ + 3x₂
3x₁ + 9x₂ 3x3 = -12
-x₁3x₂ +
x3 =
4
2xy + 2z = -4
6x3y + 6z = -12
14. a. x+10y = 2
16, a. 6x₁ + 2x₂ = -8
b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48922dd6-b6f8-4fac-84c6-05a7db5750f6%2F3c51d550-a5cf-4a2a-9199-c69263ea1472%2F8pzeag_processed.jpeg&w=3840&q=75)
Transcribed Image Text:al linear
ear sys-
s in the
mented
e lin-
aus 1.1 Introduction to Systems of Linear Equations 9
11. In each part, solve the linear system, if possible, and use the
result to determine whether the lines represented by the equa-
tions in the system have zero, one, or infinitely many points of
intersection. If there is a single point of intersection, give its
coordinates, and if there are infinitely many, find parametric
equations for them.
a. 3x - 2y = 4
6x - 4y = 9
b. 2x - 4y = 1
4x-8y = 2
c. x-2y = 0
x - 4y = 8
12. Under what conditions on a and b will the linear system have
no solutions, one solution, infinitely many solutions?
2x - 3y = a
4x - 6y= b
In each part of Exercises 13-14, use parametric equations to describe
the solution set of the linear equation.
13. a. 7x - 5y = 3
b. 3x₁5x₂ + 4x3 = 7
c. -8x₁ + 2x₂5x3 + 6x4 = 1
d. 3v8w + 2xy + 4z = 0
b. x₁ + 3x₂ - 12x3 = 3
c. 4x₁ + 2x₂ + 3x3 + x4 = 20
d. v+w+x - 5y +7z=0
In Exercises 15-16, each linear system has infinitely many solutions.
Use parametric equations to describe its solution set.
15. a. 2x-3y = 1
6x9y = 3
x3 = -4
b. x₁ + 3x₂
3x₁ + 9x₂ 3x3 = -12
-x₁3x₂ +
x3 =
4
2xy + 2z = -4
6x3y + 6z = -12
14. a. x+10y = 2
16, a. 6x₁ + 2x₂ = -8
b.
![U
-1
3
0
-9
0
0
0
-21
In each part of Exercises 7-8, find the augmented matrix for the lin-
ear system.
7.
a. - 2x₁ = 6
b. 6x₁ - x₂ + 3x3 = 4
3x₁ =
1 8
5x₂ -
X3 = 1
9x₁ = -3
C.
2x2
-11
8.
- 3x4 + x₂ = 0
= -1
6
- 3x₁
-
x₂ + x3
6x₁ + 2x₂x3 + 2x4 - 3x5 =
b. 2x₁
a. 3x₁2x₂ = -1
+ 2x3 = 1
4x₁ + 5x₂ =
3
3x₁ - x₂ + 4x3 = 7
7x₁ + 3x₂1
=
2
6x₁ + x₂
X3 = 0
C. X₁
= 1
x2
= 2
x3
= 3
9.
In each part, determine whether the given 3-tuple is a solution
of the linear system
2x₁4x₂ - X3 = 1
C. -8x₁ + 2
d. 3v-8w
14. a. x+10y =
b. x₁ + 3x₂
c. 4x₁ + 2x-
d. v+w+.
In Exercises 15-1
Use parametric e
15. a. 2x - 3y =
6x-9y=
b.
x₁ + 3x₂
3x₁ + 9x2
-X₁ - 3x₂
16. a. 6x₁ + 2x₂
3x₁ + x₂
In Exercises 17-18,
create a 1 in the upp
will not create any f
-1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48922dd6-b6f8-4fac-84c6-05a7db5750f6%2F3c51d550-a5cf-4a2a-9199-c69263ea1472%2Fcsvqebv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:U
-1
3
0
-9
0
0
0
-21
In each part of Exercises 7-8, find the augmented matrix for the lin-
ear system.
7.
a. - 2x₁ = 6
b. 6x₁ - x₂ + 3x3 = 4
3x₁ =
1 8
5x₂ -
X3 = 1
9x₁ = -3
C.
2x2
-11
8.
- 3x4 + x₂ = 0
= -1
6
- 3x₁
-
x₂ + x3
6x₁ + 2x₂x3 + 2x4 - 3x5 =
b. 2x₁
a. 3x₁2x₂ = -1
+ 2x3 = 1
4x₁ + 5x₂ =
3
3x₁ - x₂ + 4x3 = 7
7x₁ + 3x₂1
=
2
6x₁ + x₂
X3 = 0
C. X₁
= 1
x2
= 2
x3
= 3
9.
In each part, determine whether the given 3-tuple is a solution
of the linear system
2x₁4x₂ - X3 = 1
C. -8x₁ + 2
d. 3v-8w
14. a. x+10y =
b. x₁ + 3x₂
c. 4x₁ + 2x-
d. v+w+.
In Exercises 15-1
Use parametric e
15. a. 2x - 3y =
6x-9y=
b.
x₁ + 3x₂
3x₁ + 9x2
-X₁ - 3x₂
16. a. 6x₁ + 2x₂
3x₁ + x₂
In Exercises 17-18,
create a 1 in the upp
will not create any f
-1
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