Simultaneous Linear Equations Worksheets
There are times when two linear equations share an ordered pair. Under those circumstances you can use them in coordination with one another to find a common solution. A system is a group of linear equations. When a system contains equations that all share an ordered pair, we call them simultaneous. There are a number of different ways that we can use to find the ordered pair that solve the system. You will see them listed below. What that means is that when all of these lines are graphed they will intersect at that one single point. These worksheets and lessons will help us better understand how to approach and ultimately solve simultaneous linear equations.
Aligned Standard: Grade 8 Expressions and Equations - 8.EE.C.7b
- Solve the System Step-by-Step Lesson- Solve the system in each case. This is a very basic starting point for students.
- Guided Lesson - Graph the systems to find the solution for the systems.
- Guided Lesson Explanation - These are very straightforward questions for you to begin to tackle with students.
- Independent Practice - Ten problems to practice away with. Get your graph paper ready.
- Matching Worksheet - Match the systems with their graphs.
- Answer Keys - These are for all the unlocked materials above.
I start this skill in a very basic manner. A flat line is always a good place to start.
- Homework 1 - Solve this system of equations by graphing. Graph the equations, and then write the solution.
- Homework 2 - Calculate the solution by graphing.
- Homework 3 - This equation tells you that every y-value is 8. Plot some points that have a y value of 8, like (0, 8) and (1, 8), and then draw a line connecting them.
"Solving systems" always makes it sound a lot more complicated than the topic really is.
- Practice 1 - See where they all meet up?
- Practice 2 - Take it all home for you.
- Practice 3 - Make the Ys equal to each other and get this one going.
Math Skill Quizzes
For the answers, I tried to give you a snapshot of where the graph intersection is found.
- Quiz 1 - Number three and four are a cinch.
- Quiz 2 - Don't let the fractions through.
- Quiz 3 - How much does the line rise and run?
What are Simultaneous Linear Equations?
Linear equations, a relatively newer concept for you as you get into middle school, is a significant tool required to use in everyday applications. These equations are very helpful in describing a relationship between two variables in the physical world. They allow scientists to make predictions and conversions and calculate rates. Graphing linear equations make the trends that you can see in the data it produces visible. For example: y = 2x + 1. This is a linear equation.
When two linear equations contain the same variables (x and y) we can use them together to solve for these variables this is called simultaneous linear equations. Example of such two equations is: 2x - 3y = 4, 3x + y = 1. The solution a simultaneous equation is presented in the form of an ordered pair (x, y). That solution will satisfy both equations meaning that they are points that can be found on each of the equations lines when they are graphed on coordinate system.
How to Solve Simultaneous Linear Equations
There are 3 basic methods for determining an ordered pair that would satisfy both linear equations:
The steps to solve simultaneous linear equations are as follows:
Step # 1: Multiply each equation with a number that makes the leading co-efficient the same.
Step # 2: Find the difference between the two-equations. Subtract second from the first.
Step # 3: Now solve the new equation that has only one variable.
Step # 4: Substitute the value of this variable in either of the equations and find the other.
Step # 5: Write the answer in an ordered pair.
I would say this is a helpful method but does not always work perfectly if the lead coefficients are very large or odd values.
This is where you rearrange one of the equations to satisfy a single variable. For example, you make one of equations equal to x. You then plug (substitute) this value in for the x of the other equation. You then solve the equation algebraically to find an ordered pair that solves the system. The great thing about this is that you can check your answer by plugging them into both equations and see if it does in fact work.
If you graph both equations, wherever they intersect is the solution we are looking for. That ordered is the ordered pair we are looking for.