Chapter 0, Problem 57PFG

To determine

To solve the equation

Answer to Problem 57PFG

The system has no solution.

Explanation of Solution

Given information:

  $\begin{array}{l}\frac{1}{2}x-y=-1\\ x-2y=5\end{array}$

Calculation:

Let the equation be (1) and (2) respectively,

Taking (2),

  $x-2y=5$

Rearranging,

  $x=5+2y$ (3)

Put in (1),

  $\frac{1}{2}(5+2y)-y=-1$

Solving,

  $\frac{5}{2}-\frac{2}{2}y-y=-1$

It is observed that y is cancelled out, hence cannot be solved further.

The system has no solution.