To determine the nature of the solution set for the given equations, we need to analyze the equations of the lines A and B.
Line A is represented by:
x + y = 6 (Equation 1)
Line B is represented by:
x + y = 4 (Equation 2)
Let's compare the two equations:
- Both equations have the same coefficients for x and y (both are 1).
- The constants on the right side of the equations are different (6 for Line A and 4 for Line B).
- The presence of the same coefficients for x and y, but different constants, implies that the two lines are parallel to each other.
In a coordinate plane, parallel lines are lines that have the same slope but different y-intercepts; they never intersect since they run in the same direction at a fixed distance apart. Since the lines represented by these equations are parallel, there is no point (x, y) that lies on both lines at the same time.
Therefore, there is no pair of (x, y) values that can simultaneously satisfy both Equation 1 and Equation 2. In other words, the system of equations has no solution.
