The purpose of solving a system of three equations using elimination is to find the values of the variables that satisfy all three equations simultaneously. This allows us to find the intersection point, or points, of three lines, which can have various real-world applications in fields such as engineering, economics, and physics.
The process involves eliminating one variable at a time by multiplying one or both equations by a constant, and then adding or subtracting the equations to eliminate that variable. This is repeated until only two equations with two variables remain, which can then be solved using substitution or another method.
Some tips include choosing which variable to eliminate first based on coefficients (choose the variable with the smallest coefficient), making sure to multiply both equations by the same constant when eliminating, and checking the solutions by plugging them back into the original equations.
No, a system of three equations cannot always be solved using elimination. This method only works when there are three equations with three variables, and the equations are linear (no exponents). If the system is inconsistent (no solutions) or dependent (infinite solutions), elimination will not work.
Solving a system of three equations using elimination can be useful in fields such as engineering (finding the intersection point of three electrical currents), economics (determining the optimal production levels for three different products), and physics (finding the point where three forces intersect). It can also be used in everyday life, such as finding the intersection point of three streets on a map.