Answer:
Thus, option (a), (b) , (c) , (d) are correct.
The system will have no solution for all values except 12.
Step-by-step explanation:
Given a system of equation y = –2x + 4 and 6x + 3y = ?
We have to check for which value the '?' would result in a system of equations with no solution.
Consider a system of equation
For the system to have no solution the condition is,
For the given system of equation ,
Let unknown quantity be v.
y = –2x + 4 ⇒ 2x +y - 4 = 0
and 6x + 3y = v ⇒ 6x + 3y - v =0
On comparing, we get,
Substitute the values in condition for no solution , we get ,
Consider second and third ratio, we get,
Solve for v , we get,
Thus, for all values v except v = 12
The system will have no solution
at v = 12 the system will have infinite many solution.
Thus, option (a), (b) , (c) , (d) are correct.