Chapter 6, Problem 2PFA

To determine

To find: The statement that is true for the given system of equations.

Answer to Problem 2PFA

The statement B is true.

Explanation of Solution

Given information:

The system of equations is

  $3x+y=-5$

  $y+3x=4$

Statements are:

A. The system has one solution at $\left(\frac{7}{6},-\frac{1}{2}\right)$ .

B. The system has no solution.

C. The system has infinitely many solutions.

D. The system has one solution at $\left(-\frac{5}{3},9\right)$ .

Concept used:

If a system has at least one solution, then it is said to be consistent. 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.

The graph of two equations (straight lines) is shown in figure here.

Two straight lines are parallel so the will never meet, they are inconsistent, hence, the given system of equations has no solution.

The statement B is true.