Solve the system of equations If the system has no solution

Solve the system of equations. If the system has no solution, say that it is inconsistent. {x + 3y = 6 2x + 6y = 12 Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. The solution is x = y = (Type integers or simplified fractions.) B. There are infinitely many solutions. Using ordered pairs, they can be expressed as {(x, y) | x = y any real number (Simplify your answer. Type expressions using y as the variable as needed.) C.. The system is inconsistent.

Solution

Solution: (option-B)

Here;

x+3y = 6

=> x = 6-3y ----eq1

and

2x + 6y = 12

=> 2(6-3y) + 6y = 12 (by eq1)

=> 12 -6y +6y = 12

=> x can have any values to satisfy these equations

same goes for y

=> B is correct!