System of Equations
By: Ashlyn Marion
What are Systems of Equations?
System of Equations can be solved in three different ways
- graphing
- elimination
- substitution
They can be Presented in different ways also
- Word Problems
- write a system
They also can represent different things
- infinitely many
- no answer
- one answer
Finding system of equations through elimination
You can use solve by using elimination if two terms of the smae terms, but they have oppiste coefficents. you can just cancle or elimant one varible then solve for the other. then you just plug it back in and solve. The addition method of solving systems of equations is also called the method of elimination.
Finding system of Equations through substitution
You can solve by using substitution by choosing one of the equations and solving it for one variable. Then after you have solved that equation for the variable you plug the variable back into the second equation that you did not use. After you solve this equation and found what the other varible equals you have solved your problem.
Finding a System of Equations through Graphing, Write a system, and Word problems
You can use solving by elimination for large and small coefficients. All you have to do is graph where both of your problems are. the place that these two intersect is the solution for your problem.
So for example if your two points intersection point is (5,7), the solution to your problem is x = 5, and y = 7. After you find this it is best that you then plug those answers into the original problem and make sure the are correct.
Word Problems
Graphing
Write a System
A linear system of two equations with two variables is any system that can be written in the form.
Where any of the constants can be zero with the exception that each equation must have at least one variable in it.
Also, the system is called linear if the variables are only to the first power, are only in the numerator and there are no products of variables in any of the equations.
Here is an example of a system with numbers.