Question

Is this equation no solution, one solution, or infinitely may solutions

Answer 1

Given:

`\begin{gathered} x+4y=8\ldots\ldots\ldots\ldots(1) \\ y=-(1)/(4)x+2\ldots\ldots\ldots\ldots(2) \end{gathered}`

To solve for x and y:

Substitute the equation (2) in (1) we get,

`\begin{gathered} x+4(-(1)/(4)x+2)=8 \\ x-x+8=8 \\ 8=8 \end{gathered}`

Therefore, the given system has infinitely many solutions.