Solving Systems of Linear Equations by Graphing Worksheets
There are several methods that you can use to solve for the unknown variables within a system of linear equations. On this page we will focus on using graphs of these equations to locate and understand the value of these unknown variables. It is a pretty intuitive way to do. You simply plot each of the equations on a graph and find where they intersect. The intersection identifies a position where the values for both equations is the same. These worksheets and lessons focus on how to solve systems of linear equations by using the graphing method. This is one of three techniques that we use to solve these types of problems at this level.
Aligned Standard: HSA-REI.C.6
- Graphing Systems Step-by-step Lesson- We work on putting two lines together to see where we meet.
- Guided Lesson - You can solve most systems just by seeing the point at which their graph intersects.
- Guided Lesson Explanation -Please excuse the points where I drop in a random "Step 2)". Those are for patterned learners who told me it helped.
- Practice Worksheet - It is kind of neat the way I ask you the basic underlying question in six different ways with this one.
- Matching Worksheet - This makes for a very interesting review sheet of this material, as many teachers have sent me notes on over the years.
- Linear Systems - Write as a Matrix Five Pack - Make a matrices from the linear system that you are given.
- Graphing Linear Systems Five Pack - These are nicely put together. Start by solving systems graphically. Then find area of a systems and graph intercepts.
- Answer Keys - These are for all the unlocked materials above.
Homework Sheets
Remind students that they can check their work by doing them with the standard method.
- Homework 1 - Solve this system of equations by graphing. Start by graphing the line for each and then determine the solution. This is where the lines meet.
- Homework 2 - First graph the equations and then determine the solution by finding the intersection point.
- Homework 3 - Is (4, 7) a solution to this system of equations?
Practice Worksheets
It might make twice the work when check the answer, but being twice as right has it's privileges.
- Practice 1 - Find the solution to this system.
- Practice 2 - You will need to plot a solid graph here.
- Practice 3 - A point is a solution to a system of equations if plugging the point into each equation results in a true statement.
Math Skill Quizzes
I could only fit 6 on each page. I'm working on a new format that might allow up to 8.
- Quiz 1 - Write the linear systems as matrix equations.
- Quiz 2 - Prepare a graph and find where the lines intersect.
- Quiz 3 - Find the area by drawing given lines on graph paper.
How to Solve Systems of Linear Equations by Graphing
Graphs are a brilliant way to illustrate relationships between quantities and identities in data. The basic purpose of the graph is to represent data in a systematic manner that is easy to comprehend and makes more sense. Graphing has been helping children for years to make complicated data easy and so it is important to learn about graphing all kinds of equations.
A linear graph is one that is formed out of a linear equation. It forms a straight line, hence the name. These types of equations usually have two unknown variables, x, and y. There are many situations where multiple linear equation will form a system where all of their unknown variables are shared, meaning that the unknowns all have the same value.
Since simultaneous equations involve two or more equations, you can graph both them and see where on the graph they intersect each other. The point where the x and y coordinates of these equations intersect will be the solution to the system of equations. This point of intersection is the only point that covers both the lines so it's the only coordinate combination of x and y values that makes each of the equations true. Here it is important to remember that the intersection point of both the equations is where your solution lives.
When Should You Use Graphs to Solve Systems?
Systems are a series of items that display a high level of interdependency with one another. In most cases when we are approaching systems in math, we are discussing two interrelated equations. When we are looking for a solution to a system, we are trying to get an ordered pair that solves equations. That order pair would represent where the two lines of the graphed equation would meet or intersect. You can find this point in a number of different ways. You can use a method called substitution where you remove all but one of the variables in an equation and solve the equation from there. You achieve this by isolating the other variable in the equation and then substitute that value into the other equation. Depending on the math involved, this is usually my go to method, but there are times that when I first set it up, there is some really complex calculations or values which could lead to inaccuracies. Another common method for solving systems is called elimination. This is where you combine or subtract the equations from one another. While this is super easy, when it is set to work, it does not also lend itself to be possible. When both of the other techniques do not suit your situation, the graphing method is best. It is a bit more time consuming than the other two methods and this is why it shouldn’t be the only tool in your toolbox. The beauty of the graphing method is that you can self-check your solutions. Once you establish an ordered pair that should work for both equations, just substitute it for the variables in the equations and they should work out. If not, go back and check your math.