Chapter 6.5, Problem 28HP

To determine

To explain when to use which method to solve system of equations.

Explanation of Solution

By Analyzing the coefficients of the given system of equations, the method that is best suited can be determined.

Substitution Method:

If one of the variables in either of the equations has a coefficient of 1 or -1, substitution could be used.

Elimination Method:

If a variable in both the equations has coefficients that are opposites, then elimination using addition is the best way to solve the system of equations.

If a variable in both the equations has coefficients that are same, then elimination using subtraction is the best way to solve the system of equations.

If both the above conditions fail, elimination using multiplication could be more convenient.

Graphing Method:

If the given system of equations are in slope-intercept form, i.e. $y=mx+c$ , then graphical method can be the suitable one.

Conclusion:

Therefore, the given system of equations can be solved through any of the methods if the conditions are satisfied.