Solving Systems Of Equations By Elimination Worksheet Pdf
If you are a high school or college student, you know that math can be challenging, especially when it comes to solving systems of equations. However, there is a method called "elimination" that can make it easier to solve these types of problems. In this article, we will be discussing how to solve systems of equations by elimination and will provide a downloadable worksheet in PDF format that you can use to practice.
What is a System of Equations?
Before you can learn how to solve a system of equations by elimination, you need to understand what a system of equations is. Simply put, a system of equations is a set of two or more equations that you need to solve at the same time. Typically, we use systems of equations to solve problems that involve more than one variable. For example:
If you are shopping for books and magazines, you might buy 3 books and 2 magazines for $35. Later, you might buy 2 books and 1 magazine for $18. How much does a book cost? How much does a magazine cost?
This problem can be represented by a system of equations:
3b + 2m = 35 (Equation A)
2b + 1m = 18 (Equation B)
Where 'b' is the cost of a book and 'm' is the cost of a magazine.
Solving Systems of Equations By Elimination
The elimination method is one of the most common ways to solve a system of equations. It involves adding or subtracting the equations to eliminate one of the variables. Here's how the process works:
1. Look at the two equations and decide which variable you want to eliminate.
2. Multiply one or both equations by a constant so that the coefficients of that variable are equal in both equations. For example, if you want to eliminate 'm', you might multiply Equation A by -1 to get:
-3b - 2m = -35 (Equation C)
2b + 1m = 18 (Equation B)
Notice that the coefficient of 'm' in Equation A is now -2 while the coefficient of 'm' in Equation B is 1. If we add these two equations, the 'm' variable will be eliminated:
-3b - 2m + 2b + 1m = -35 + 18
-b = -17
b = 17
Now that we know that a book costs $17, we can substitute that value into one of the original equations to find the cost of a magazine:
3(17) + 2m = 35
2m = 35 - 51
2m = -16
m = -8
Therefore, a magazine costs $8.
Downloadable Worksheet PDF
To practice solving systems of equations by elimination, we have created a downloadable worksheet in PDF format. This worksheet includes several problems of varying difficulty and provides step-by-step instructions on how to solve them. You can use this worksheet to practice and improve your skills.
Conclusion
Solving systems of equations by elimination can be a challenging process, but with practice, you can become proficient at it. By using the downloadable worksheet provided in this article, you can improve your skills and work towards solving more complex problems. Remember to take your time, pay attention to the details, and practice regularly.