 Hello students, let's work out the following problem. It says for what value of a the system of given linear equations has no solution So let's now move on to the solution the given equations are a x plus 3 y is equal to a minus 3 and 12 x plus a y is equal to a Now we have to find the value of a For which the system of equation has no solution now for no solution A1 upon a2 is Equal to b1 upon v2, but it is not equal to c1 upon c2 That is if we are given two equations Two linear equations a1 x plus b1 y is equal to c1 and a2 x plus b2 y is equal to c2 Then for no solution a1 upon a2 is equal to b1 upon v2, but it is not equal to c1 upon c2 you must remember this and write this while using While solving the question So now A1 is a a2 is 12 is equal to b1 that is 3 Upon v2 which is again a Is not equal to c1 which is a minus 3 Upon c2 which is a now we'll use this to find the value of a now using first two we have a upon 12 is equal to 3 upon a and Using second and third we have 3 upon a is not equal to a minus 3 upon a We first use first and second and then we use second and third Now from this cross multiplying we have a square is equal to 12 into 3 that is 36 and from this we have 3 a not equal to a into a minus 3 Now a square is equal to 36 that means a is equal to plus minus under the root 36 and From this we have 3 a Not equal to a square minus 3 a so this implies a square Minus 3 a Minus 3 a is not equal to 0 and this implies a square minus 6 a is not equal to 0 and this implies a into a minus 6 is not equal to 0 so From this we have a is not equal to 0 and a minus 6 is not equal to 0 and this implies a is not equal to 0 and a is not equal to 6 and From this we have a is equal to plus minus 6 but here We have obtained the fact that a is not equal to 6 right So here also a is equal to is not equal to 6 So the only possible value of a is minus 6 Therefore a is equal to minus 6 So a is equal to minus 6 is the required value of a So this completes the question and the session my for now take care have a very nice day