Sure, I can provide you with three examples of systems of equations, one for each method of solving: graphing, substitution, and elimination.
1. Graphing:
Let's say we have the following system of equations:
Equation 1: y = 2x + 3
Equation 2: y = -x + 5
Graphing would be a good method to solve this system because we can plot the lines represented by each equation on a graph and find the point where they intersect, which represents the solution.
2. Substitution:
Consider the following system of equations:
Equation 1: 2x + y = 10
Equation 2: 3x - y = 4
Substitution would be a suitable method to solve this system because we can solve one equation for one variable and substitute it into the other equation to find the value of the remaining variable.
3. Elimination:
Let's take this system of equations as an example:
Equation 1: 3x + 2y = 8
Equation 2: 2x - 3y = 1
Elimination would be an effective method to solve this system because we can manipulate the equations by multiplying them by appropriate factors to eliminate one of the variables when we add or subtract the equations.
These are just examples to illustrate the different methods of solving systems of equations. The choice of method depends on the specific equations and the most efficient approach for finding the solution.