Answer:
Explanation:
To have a system with one solution, the two equations should not be multiples of each other.
We can check if they are multiples by dividing the second equation by 3, which gives:
x - 6y = 4
x - 6y = 4/3
Since the two equations are multiples of each other, they represent the same line and have infinite solutions. To change the system to one with a unique solution, we need to change one of the coefficients or constants in such a way that the resulting equations are not multiples of each other.
Let's add 2 to the constant in the first equation:
x - 6y = 6
Now let's subtract 2 from the constant in the second equation and simplify:
3x - 18y = 2
x - 6y = 2/3
The new system is:
x - 6y = 6
3x - 18y = 2
This system does not have infinite solutions and has a unique solution.