Question

Show that the system of equations 6x + 5y = 11, 9x + 15/2y = 21 has no solution

Answer 1

Given: Two equations 6x + 5y = 11, 9x + 15/2y = 21

To find: Show that the system of equations 6x + 5y = 11, 9x + 15/2y = 21 has no solution.

Solution:

• Now we have given the equations as:

                  6x + 5y = 11, 9x + 15/2y = 21

• We can rewrite it as

                  6x + 5y - 11 = 0 ….(i)  

                  9x + 15/2 y - 21 = 0 …(ii)

• Now this system is in the form of:

                  a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0  

• Here, a1 = 6, b1 = 5, c1 = -11 and a2 = 9, b2 = 15/2 , c2 = -21  

• We have given system has no solution, so:

                  a1/a2 = 6/9 = 2/3

                  b1/b2 = 5 / 15/2 = 2/3

                  c1/c2 = -11/-21 = 11/21

• Here a1/a2 = b1/b2 ≠ c1/c2

• Hence condition of no solution satisfies.

Answer:

              So the system has no solution .