A system of equations is a set of two or more equations with the same variables.
The goal is to find the values of the variables that satisfy all the equations in the system simultaneously.
The solution to a system of equations is an ordered pair\$(x, y)\$ that makes both equations true.
Solving Systems of Equations
There are several methods to solve systems of equations:
- Substitution Method
- Elimination Method
- Graphical Method
Substitution Method
The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.
The substitution method is often easier when one of the equations is already solved for one variable.
The elimination method is often more efficient when the coefficients of one of the variables are already opposites or can be easily made opposites by multiplication.
The graphical method provides a visual representation of the solution, but it may not be precise for non-integer solutions.
How do different methods for solving systems of equations reflect different ways of thinking about mathematical problems? What are the advantages and limitations of each method?
