Final answer:
By adding the two given equations, we eliminate x and z, resulting in the solution that y equals 7.
Step-by-step explanation:
To determine the value of y from the equations x - 2y + z = 5 and -x + 3y - z = 2, a strategic combination is employed. By adding the two equations, x and z terms cancel out, simplifying to -y = 7. Thus, the value of y is determined to be 7. This approach leverages the addition of equations to eliminate specific variables, revealing a straightforward solution for the targeted variable, y, in this system of linear equations. Such methods are foundational in linear algebra and provide systematic ways to solve systems of equations by isolating individual variables through algebraic manipulations.