30 20 10 -10 -20 -10 Linear equations in n variables: a,x, + a,x, + a,x, ++ a + a,x, = b (a,, a, a a,: constants) Solutions: Graph: b-a,x, -a,x, a X,, X3, X X Hyperplane in n dimensions a. Systems of Linear Equations Case Li (unique solution) * + 2y = 3 4x + 9y =8 10
30 20 10 -10 -20 -10 Linear equations in n variables: a,x, + a,x, + a,x, ++ a + a,x, = b (a,, a, a a,: constants) Solutions: Graph: b-a,x, -a,x, a X,, X3, X X Hyperplane in n dimensions a. Systems of Linear Equations Case Li (unique solution) * + 2y = 3 4x + 9y =8 10
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 84E
Related questions
Question
I need help understanding how to use the n variables formula and the 3 equations formula in my professors
Transcribed Image Text:Math 245
2 / 7
100%
+ | A O
1
30
20-
10
- 10
-20
- 10
10
- 5
- 10
Linear equations in n variables:
a,X, + a,x2 +azx3 + • ··+ a,-Xn-1 + a „x, = b
(а,, а>, аз»
constants)
Solutions:
Graph:
b-a,x - a,X2
a
n-1n-1
X1, X2, X3, •…., Xn-12
Hyperplane in n dimensions
an
Systems of Linear Equations
Case I: (unique solution)
x + 2y = 3
4х + 9у %3D 8
4
||
-10
10
15
5
-2-
-4
II
Transcribed Image Text:Math 245
1 / 7
100%
+ | A O
(-
Linear Equations and Systems
Linear equations in one variable:
1
ax = b
(a,b: constants)
Solution:
x =
(a ±0)
Linear equations in two variables:
ах + by %3D с
(a,b,c: constants)
Solutions:
Graph:
c-by
С — ах
х,
b
or
Line in 2 dimensions
а
1
- 1
4
Linear equations in three variables:
ах + by + cz %3D d
(a,b,c,d: constants)
Solutions:
Graph:
d - ах -by
or
d — ах — Cz
х,
х, у,
Plane in 3 dimensions
or ...
5
b
II
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage