Question

In the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:

x - 2y - 8 = 0

5x - 10y - 10 = 0

Answer 1

The given system of equation may be written a

x - 2y - 8 = 0

5x - 10y - 10 = 0

The given system if equation is of the form

`a_1x + b_1y + c_1 = 0`

`a_2x + b_2y + c_2 = 0`

Where `a_1 = 1, b_1 = -2, c_1 = -8`

And `a_2 = 5, b-2 = -10, c_2 = -10`

We have,

`a_1/a_2 = 1/5`

`b_1/b_2 = (-2)/(-10) = 1/5`

And `c_1/c_2 = (-8)/(-10) = 4/5`

Cleary `a_1/a_2 = b_2/b_2 != c_1/c_2`

So, the given system of equation has no solution