Combining equations inside a system entails summing their left-hand sides and their right-hand sides individually to create a brand new equation. As an example, given the system x + y = 5 and 2x – y = 1, summing the left sides (x + y) + (2x – y) yields 3x, and summing the correct sides 5 + 1 leads to 6. The ensuing equation is 3x = 6.
This course of is key in fixing methods of equations. It permits for the elimination of variables, simplifying the system and enabling the dedication of options. This method seems throughout various mathematical fields, from fundamental algebra to linear programming and past, proving important for fixing complicated issues. Its historic roots lie throughout the improvement of algebraic strategies, essential for developments in varied scientific and engineering disciplines.
