Chapter 6.3, Problem 19P

Solve each system using elimination. Tell whether the system has one solution, infinitely many solutions, or no solution.

$x-3y=-7$

$2x=6y-14$

To determine

To solve: the system using elimination and suggest whether the system has one solution, infinitely many solutions, or no solution.

  $\begin{array}{l}x-3y=-7\\ 2x=6y-14\end{array}$

Answer to Problem 19P

After elimination system will have infinitely many solutions, which are consistent but dependent.

Explanation of Solution

Given information:

  $\begin{array}{l}x-3y=-7\\ 2x=6y-14\end{array}$

Calculation:

In order to solve two system using elimination, we multiply first equation by 2 and rearrange the system as follows:

  $\begin{array}{l}2x-6y=-\mathrm{14........}(i)\\ 2x-6y=-\mathrm{14.........}(ii)\end{array}$

As both the equations are same there are infinitely many solutions which are consistent but dependent.