Final answer:
The system of linear equations -2x + y = 1 and 2x - y = 3 has no solution because adding both equations results in a contradiction, indicating that the lines are parallel.
Step-by-step explanation:
To solve the system of linear equations given by -2x + y = 1 and 2x - y = 3, we can add the two equations together to eliminate both x and y variables because the coefficients of x in both equations are opposite numbers as well as the coefficients of y.
By adding, we get:
- (-2x + 2x) + (y - y) = 1 + 3
- 0 + 0 = 4
This gives us a contradiction because 0 does not equal 4. Therefore, there is no solution to the system, and this means that the two lines represented by the equations are parallel and never intersect.