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