Chapter 0, Problem 59PFG

To determine

To solve the system of equations

Answer to Problem 59PFG

The equation has infinitely many solutions.

Explanation of Solution

Given information:

  $\begin{array}{l}\frac{1}{3}x-3y=-4\\ x-9y=-12\end{array}$

Calculation:

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

Taking (2),

  $x-9y=-12$

Rearranging,

  $x=-12+9y$ (3)

Put in (1)

  $\frac{1}{3}(-12+9y)-3y=-4$

Solving,

  $\frac{-12}{3}+\frac{9y}{3}-3y=-4$

So,

  $-4+3y-3y=-4$

It is observed that 3y cancels, so, the equation has infinitely many solutions.