Combining two equations through addition generates a new equation that reflects the combined relationships expressed by the original equations. For instance, adding the equations x + y = 5 and 2x – y = 4 yields 3x = 9. This process is fundamental in solving systems of equations, allowing for the elimination of variables and the determination of solutions that satisfy all involved equations.
This technique is crucial in diverse fields like physics, engineering, economics, and computer science. It provides a powerful tool for modeling complex systems, analyzing data, and making predictions. Historically, the development of methods for solving systems of equations marked a significant advancement in mathematics, enabling solutions to problems previously intractable. This ability to manipulate and combine equations laid the groundwork for many subsequent mathematical innovations.
