Question

How many solutions does the system of equations `7x - 7y = - 6` and `11x - 11y = 15` have?

Answer 1

There is no solution for the two equations.

Explanation:

Usually we would solve for `x` and `y`, but the question asks
how many solutions there are.

Because the coefficients are the same in each equation, let's use a different method.

`7x-7y=-6color(white)(......................)11x-11y = 15`

`7(x-y) = -6color(white)(.....................)11(x-y) = 15`

`x-y = -6/7color(white)(......................)x-y = 15/11`

Now we clearly have problem because we have 2 different answers for `x-y`

The difference between the same numbers cannot be different.

`-6/7 !=15/11`

This is an indication that there is no solution for the two equations.