EXERCISE 3. Consider the system 12 + 3r3 12 - 13 + 2r4 = 2 I4 = 1 (a) Described the solution set where the variables r3 and x4 are free. (b) Described the solution set where the variables r2 and 14 are free. (c) Show that the two solution sets obtained are equivalent [ {(3 – 2s – t, 2+ s – 2t, s, t)\s, t € R}; {(7 – 2u – 5v, u, -2+ u + 2v, v)|u, v € R}; set u = 2+ s – 2t, v = t, the solution set in part(b) is identical to the solution set in part (a) ]
EXERCISE 3. Consider the system 12 + 3r3 12 - 13 + 2r4 = 2 I4 = 1 (a) Described the solution set where the variables r3 and x4 are free. (b) Described the solution set where the variables r2 and 14 are free. (c) Show that the two solution sets obtained are equivalent [ {(3 – 2s – t, 2+ s – 2t, s, t)\s, t € R}; {(7 – 2u – 5v, u, -2+ u + 2v, v)|u, v € R}; set u = 2+ s – 2t, v = t, the solution set in part(b) is identical to the solution set in part (a) ]
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 3GP
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Can someone explain the concept of free variable and how to go about approaching such questions?
![EXERCISE 3. Consider the system
12 + 3x3
1
T3
+ 2x4
2
(a) Described the solution set where the variables x3 and x4 are free.
(b) Described the solution set where the variables r2 and a4 are free.
(c) Show that the two solution sets obtained are equivalent
[ {{3 – 2s – t, 2 + s – 2t, s, t)|s, t E R};
{(7 – 2u – 5v, u, –2+ u + 2v, v)|u, v E R};
set u = 2+s – 2t, v = t, the solution set in part(b) is identical to the solution set in
part (a) ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e6a9b5e-7be7-44fa-a640-7da6aaa32842%2F2e61575a-d797-4b2b-8cdd-11fe2489460f%2F7z11kzm_processed.png&w=3840&q=75)
Transcribed Image Text:EXERCISE 3. Consider the system
12 + 3x3
1
T3
+ 2x4
2
(a) Described the solution set where the variables x3 and x4 are free.
(b) Described the solution set where the variables r2 and a4 are free.
(c) Show that the two solution sets obtained are equivalent
[ {{3 – 2s – t, 2 + s – 2t, s, t)|s, t E R};
{(7 – 2u – 5v, u, –2+ u + 2v, v)|u, v E R};
set u = 2+s – 2t, v = t, the solution set in part(b) is identical to the solution set in
part (a) ]
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