Question

36. The system of two linear equations given by:2x+4y=1 and x=-2y+1/2hasa. No solutionsb. An infinite number of solutionsc. Possibly several solutionsd. Exactly one solutione. None of the above

Answer 1

Given:

`\begin{gathered} 2x+4y=1\ldots\ldots\ldots\ldots\text{.}(1) \\ x=-2y+(1)/(2)\ldots\ldots\ldots\ldots\text{.}(2) \\ \\ R\text{ earranging equation (2);} \\ x+2y=(1)/(2) \\ \text{Multiplying the equation all through by 2;} \\ 2x+4y=1\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}`

Since both equations are mathematically the same, then the graph of both linear equations are shown below;

From the above graph given, the system of two linear equations has an infinite number of solutions.

The correct answer is option B.