Which method(s) can be used to solve a system of equations? Select all that apply.
modeling
distributing
substitution
addition
graphing
formulas
substitution, addition, graphing, formulas
The methods that can be used to solve a system of equations are:
1. Substitution: In this method, one equation is solved for one variable and then substituted into the other equation. This allows for solving for the other variable.
2. Addition (or elimination): In this method, both equations are added or subtracted in a way that eliminates one of the variables. This allows for solving for the remaining variable.
3. Graphing: In this method, the system of equations is graphed on a coordinate plane. The intersection point of the two lines represents the solution to the system of equations.
So, the correct options are:
- Substitution
- Addition (or elimination)
- Graphing
The following methods can be used to solve a system of equations:
1. Substitution: In this method, you solve one equation for one variable and substitute that expression into the other equation. This way, you create a new equation with only one variable, which can be solved to find its value. Once you have the value of one variable, you substitute it back into one of the original equations to find the value of the other variable.
2. Addition (also known as the elimination method or the method of adding or subtracting equations): In this method, you add or subtract the equations in a way that eliminates one of the variables. By doing so, you are left with a new equation that only involves one variable, which can be solved. Then, like the substitution method, you substitute the found value back into one of the original equations to find the value of the other variable.
3. Graphing: In this method, you graph each of the equations on a coordinate plane. The point(s) where the graphs intersect represent the solutions to the system of equations. By analyzing the graph, you can determine the values of the variables.
These are the three common methods used to solve a system of equations. Modeling, distributing, and using formulas may be helpful steps within these methods, but they are not standalone methods of solving systems of equations.