What are two symbolic techniques used to solve linear equations? Which do you feel is better
What are two symbolic techniques used to solve linear equations
Two symbolic techniques commonly used to solve linear equations are substitution and elimination.
1. Substitution: In this technique, we solve one equation for one variable and substitute that expression into the other equation. The result is a new equation with only one variable, which can be solved to find its value. This value can then be substituted back into either of the original equations to find the value of the other variable.
2. Elimination: In this technique, we manipulate the equations by adding or subtracting them together in a way that eliminates one of the variables. By adding or subtracting the equations, the coefficients of one variable are made equal, which allows us to eliminate that variable by subtracting one equation from the other. This results in a simplified equation with only one variable, which can then be solved.
As for which technique is better, it depends on the specific equations and the preferences of the person solving them. Substitution is often preferred when one equation can easily be solved for one variable, making substitution straightforward. Elimination, on the other hand, is often preferred when the coefficients of one variable can be easily manipulated to eliminate it from the equations. Both techniques are valid and widely used in mathematics.