Chapter 6.3, Problem 35HP

To determine

To find the solution of the system of equations if the sum of the equations is 0 = 2

Answer to Problem 35HP

False

Explanation of Solution

Consider the equations $2x+y=5$ and $-2x-y=3$ .

The sum of the equations is 0 = 2. When the lines are written in slope-intercept form,

  $y=-2x+5$

  $y=-2x+3$

Both the lines have a slope of -2.

Since the lines have the same slope and different y intercepts, the lines will be parallel lines to each other.

Also, Parallel lines do not intersect and have no points in common.

Therefore, there is no solution.

The system of equations is inconsistent.

Generally, the system of inconsistent equations represents parallel lines.