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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
Solution
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
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