Question

The system is x-6y =4, 3x-18y=4. Change in constant or coefficient to make a new system with one solution

Answer 1

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.