Solve each of the following systems of equations in R.
Question 1:
Answer:
Given
Case I:
Case II:
Therefore the solution set is
Question 2:
Answer:
Given
Therefore the solution set is
Question 3:
Answer:
Given
Therefore the solution set is
Question 4:
Answer:
Given
Case I: When
Case II: When
There is no possible solution. Therefore
Combining Case I and Case II we get the solution set as
Question 5:
Answer:
Given
Case I: When
Therefore
Case I(a):
Case I(b):
Therefore the solution set in Case I is
Case II: When
Therefore
Case II(a):
Case II(b):
Therefore the solution set in Case II is
Combining both Case I and Case II, we get the complete solution set as
Question 6:
Answer:
Given
Case I: When
Case I(a):
Case I(b):
Therefore the solution set in Case I and is
Case II: When
Case II(a):
Case II(b):
Therefore the solution set in Case I and is
Combining both Case I and Case II, and we get the complete solution set as
Question 7:
Answer:
Given
Case I:
Therefore the solution set for Case I is
Case II:
Case II(a):
Case II(b):
Combining both Case I and Case II, and we get the complete solution set as
Question 8:
Answer:
Given:
For
when
when
For
when
when
For
when
when
Case I: When
Hence the solutions set is
Case II: When
Hence the solutions set is null.
Case III: When
Hence the solutions set is null.
Case IV: When
Hence the solutions set is
From all the four cases the solution set is
Question 9:
Answer:
Given:
Case I: When
Therefore
Case I(a):
Therefore the solution set is null set.
Case I(b):
Therefore the solution set is .
Therefore the solution set in Case I and is
Case II: When
Therefore
Case II(a):
Therefore the solution set is .
Case II(b):
Therefore the solution set is null.
Therefore the solution set in Case I and is
Combining both Case I and Case II, and we get the complete solution set as
Question 10:
Answer:
Given:
Case I: When
Case I(a):
Therefore the solution set is .
Case I(b):
Therefore the solution set is along with is
.
Therefore the solution set in Case I is
Case II: When
Case II(a):
Therefore the solution set is .
Case II(b):
Therefore the solution set is .
Therefore the solution set in Case I is
Combining both Case I and Case II, and we get the complete solution set as
Question 11:
Answer:
Given:
When
When
Similarly,
When
When
Case I: When
Case II: When
This is not possible. Therefore
Case III: When
Therefore
Combining all the three cases, the solution set is
Question 12:
Answer:
Given
For
When
When
Hence the solution set for the first equation is
For
When
When
Hence the solution set for the first equation is
Combining the two cases, we get the solution set as
Question 13:
Answer:
Therefore the solution set will be