How To Graph A Set
Graphing Systems of Equations
This is the starting time of four lessons in the System of Equations unit. We are going to graph a system of equations in order to find the solution.
REMEMBER: A solution to a system of equations is the point where the lines intersect!
We volition begin graphing systems of equations past looking at an example with both equations written in slope intercept form. This is the easiest blazon of problem!
Case ane: Graphing Systems of Equations
Graph the following arrangement of equations and find the solution.
y = -3x + 2
y = 2x - 3
Solution
Now we are going to look at a system of equations where but one of the equations is written in gradient intercept course. The other equation is written in standard form.
So... what do you lot call back we need to practise first?
Instance 2: What Happens When an Equation is Not Written in Slope Intercept Form?
Graph the system of equations and detect the solution.
y = i/2x - iii
3x + 2y = 2
Solution
Now we will look at an example where there is no solution to the arrangement of equations. Take annotation of what the graph looks similar and why at that place might non be a solution.
Example 3: No Solution
Find the solution to the system of equations by graphing.
y = -one/2x + 4
y = -1/2x - 6
Solution
Tip
Whenever ii equations have the same slope they volition be parallel lines.
Parallel lines NEVER intersect. Therefore, the organization of equations will Not have a solution!
Our last example demonstrates 2 unlike things. The beginning is that there is more than one way to graph a organization of equations that is written in standard form.
The 2nd is that sometimes a system of equations is actually the same line, graphed on top of each other.
In this case, yous will see an space number of solutions. Information technology may be helpful for y'all to review the lesson on using x and y intercepts for this case.
Instance 4: Infinite Solutions
Graph the following organisation of equations and identify the solution.
2x - y = 8
6x - 3y = 24
There are two ways to graph a standard course equation:
- Rewrite the equation in gradient intercept grade.
- Find the x and y intercepts.
When you are graphing a system of equations that are written in standard form, you can use either method.
For this particular example, we volition discover the x and y intercepts.
Solution
Did y'all notice that both equations had the same x and y intercept?
This is considering these two equations represent the aforementioned line. Therefore, one is graphed on height of the other.
In this case, the system of equations has an infinite number of solutions! Every indicate on the line is a solution to both equations.
Yous've at present seen all dissimilar strategies for graphing a system of equations and you've experienced what a graph looks like when at that place is no solution and when there are an infinite number of solutions!
If you'd like to practice a few systems of equations bug on your ain, visit our Graphing Systems of Equations Do Page.
In the next lesson, you volition acquire another way of solving a system of equations. You will solve a arrangement using substitution.
- Home >
- System of Equations >
- Graphing Systems
Need More than Help With Your Algebra Studies?
Get admission to hundreds of video examples and practice problems with your subscription!
Click here for more data on our affordable subscription options.
Non ready to subscribe? Register for our Gratuitous Pre-Algebra Refresher course.
ALGEBRA CLASS Due east-COURSE MEMBERS
Click hither for more than information on our Algebra Grade eastward-courses.
Need Aid? Endeavor This Online Calculator!
Chapter Products...
On this site, I recommend only ane product that I utilise and dearest and that is Mathway If you make a buy on this site, I may receive a minor commission at no toll to you.
Source: https://www.algebra-class.com/graphing-systems-of-equations.html
0 Response to "How To Graph A Set"
Post a Comment