Chapter 6, Problem 4PT

To determine

To find: The number of solutions of given system of equations using graph and if it has solution, name it.

Answer to Problem 4PT

The given system of equations has infinitely many solutions which are dependent.

Explanation of Solution

Given information:

The given system of equations is

  $2x+3y=4$ , $2x+3y=-1$

Concept used:

If a system has at least one solution, then it is said to be consistent. If a consistent system of equations has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent, when graphed such equations, represent the same line.

If a system has no solution, it is said to be inconsistent .The graphs of such equations do not intersect, i.e., graphs are parallel.

Graph:

The graphs of given equations $2x+3y=4$ , and $2x+3y=-1$ are shown in Figure-1 here.

From the graph of equations we see that the equation $2x+3y=4$ and $2x+3y=-1$ represent parallel straight lines, they do not intersect.

Thus, the given system of equations $2x+3y=4$ , $2x+3y=-1$ does not have a solution.

Conclusion:

The given system of equations $2x+3y=4$ , $2x+3y=-1$ does not have a solution.