Chapter 6.3, Problem 22P

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

$5x+y=15$

$3y=-15x+6$

To determine

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

  $\begin{array}{l}5x+y=15\\ 3y=-15x+6\end{array}$

Answer to Problem 22P

As lines are parallel, we have no solution.

Explanation of Solution

Given information:

  $\begin{array}{l}5x+y=15\\ 3y=-15x+6\end{array}$

Calculation:

In order to solve two system using elimination, we multiply first equation by 3 and rearrange the system as follows:

  $\begin{array}{l}+15x+3y=\mathrm{45........}(i)\\ +15x+3y=\mathrm{6.........}(ii)\end{array}$

As both equations are parallel, we have no solution, which are inconsistent but independent.