In solving a simultaneous equation, what is the primary goal?

The primary goal in solving a simultaneous equation is to find the solution that satisfies both equations. This means identifying a set of values for the variables that make both equations true at the same time. In the context of simultaneous equations, often represented graphically, this solution corresponds to the point where the graphs of the equations intersect.

When two equations are graphed, the intersection point represents the values of the variables that meet the conditions set by both equations. If this intersection exists, it indicates a unique solution; if the lines are parallel, there is no solution; and if they are the same line, there are infinitely many solutions. Therefore, successfully solving the simultaneous equations ensures that both equations hold true with the identified values, making this the correct focus of the process.