Consider the following three systems of linear equations. System A System B -5x+3y=3 [A1] - 5x+3y=3 [B1] -8x+7y=-15 [A2] 2x+y=-21 [B2] Answer the questions below. For each, choose the transformation and then fill in the blank with the correct number. The arrow (→) means the expression on the left becomes the expression on the right. (a) How do we transform System A into System B? O× Equation [A1] ox Equation [A2] X o I x Equation [A1] + Equation [A2] Equation [B2] o D x Equation [B1] o x Equation [A2] + Equation [A1] → Equation [B1] o Equation [B1] (b) How do we transform System B into System C? × Equation [B2] X Equation [B2] - Equation [C1] System C -11x=66 [C1] 2x+y=-21 [C2] Equation [C2] X Equation [B1] + Equation [B2] Ox Equation [B2] + Equation [B1] X 1 - Equation [C2] Equation [C1] 8 08 X

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following three systems of linear equations.
System B
-5x+3y=3 [A1]
-5x+3y=3 [B1]
8x+7y=-15 [A2] 2x+y=-21 [B2]
System A
Answer the questions below.
For each, choose the transformation and then fill in the blank with the correct number.
The arrow (→) means the expression on the left becomes the expression on the right.
(a) How do we transform System A into System B?
Ox Equation [A1]
X
ox Equation [A2]
X
O
Ox Equation [A1] + Equation [A2]
X
o D
O
Equation [B1]
Equation [B2]
X Equation [B1]
(b) How do we transform System B into System C?
-
x Equation [A2] + Equation [A1] Equation [B1]
System C
-11x=66 [C1]
2x+y=-21 [C2]
Equation [C1]
0 x Equation [B2] Equation [C2]
Ox Equation [B1] + Equation [B2]
X
Equation [B2]
→
Equation [C2]
O
0 x Equation [B2] + Equation [B1] Equation [C1]
8 08
X
Transcribed Image Text:Consider the following three systems of linear equations. System B -5x+3y=3 [A1] -5x+3y=3 [B1] 8x+7y=-15 [A2] 2x+y=-21 [B2] System A Answer the questions below. For each, choose the transformation and then fill in the blank with the correct number. The arrow (→) means the expression on the left becomes the expression on the right. (a) How do we transform System A into System B? Ox Equation [A1] X ox Equation [A2] X O Ox Equation [A1] + Equation [A2] X o D O Equation [B1] Equation [B2] X Equation [B1] (b) How do we transform System B into System C? - x Equation [A2] + Equation [A1] Equation [B1] System C -11x=66 [C1] 2x+y=-21 [C2] Equation [C1] 0 x Equation [B2] Equation [C2] Ox Equation [B1] + Equation [B2] X Equation [B2] → Equation [C2] O 0 x Equation [B2] + Equation [B1] Equation [C1] 8 08 X
Expert Solution
Step 1: Define the problem.

Given: 

table row blank blank cell System space straight A colon space end cell row blank blank cell open curly brackets table row cell negative 5 straight x plus 3 straight y equals 3 space space space space space space space space space space space space open square brackets straight A subscript 1 close square brackets end cell row cell negative 8 straight x plus 7 straight y equals negative 15 space space space space space space open square brackets straight A subscript 2 close square brackets end cell end table close end cell row blank blank cell System space straight B colon space end cell row blank blank cell open curly brackets table row cell negative 5 straight x plus 3 straight y equals 3 space space space space space space space open square brackets straight B subscript 1 close square brackets end cell row cell 2 straight x plus straight y equals negative 21 space space space space space space space space open square brackets straight B subscript 2 close square brackets end cell end table close end cell row blank blank cell System space straight C colon space end cell row blank blank cell open curly brackets table row cell negative 11 straight x equals 66 space space space space space space space space space space open square brackets straight C subscript 1 close square brackets end cell row cell 2 straight x plus straight y equals negative 21 space space space space space space space open square brackets straight C subscript 2 close square brackets end cell end table close end cell end table

To Find: 

(a) To transform system A into system B.

(b) To transform system B into system C.

steps

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