Systems of Linear Equations: Elimination
Systems of Linear Equations: Elimination
Introduction:
A system of equations simply means that you are comparing multiple equations. In this lesson we will look at how to solve ( find the intersection of ) two linear equations using a process known as elimination. This will give the same result as solving by substitution but sometimes it can be easier.
At Emily's school there is a terrarium with a collection of insects (6 legs) and spiders (8 legs). Emily counts the creatures and finds out there are 21 bodies. Her friend, Ziva, counts 142 legs all together. How many spiders and how many insects are there in the terrarium?
i+s=21 because there are 21 insects and spiders all together.
6i+8s=142 because there are 6 legs for each insect and 8 for each spider.
To start with we will need to make the coefficient on one of the variables match. In this case we will use the insects because it will keep the numbers smaller but it doesn't matter which one you use. To do this we will multiply everything in the first equation by 6.
6i+6s=126
- 6i+8s=142
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0i+-2s=-16
We can then subtract the variables. 6i-6i results in the them canceling out. 6s-8s=-2s and 126-142=-16. We can then divide both sides by -2 which will give s=8. This means there are 8 spiders and because there are a total of 21 creatures there must be 13 insects (21-8=13).
There are 13 insects and 8 spiders.
The whole point of the elimination method is to eliminate one of the variable by addition or subtraction. In the first example subtraction was used but if one of the variables you want to eliminate is a negative then you can use addition such as the following example.
x+2y=5
+ 4x-2y=20
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5x+0y=25
5x=25
x=5
The 5 can then replace the x in the first equation to give 5+2y=5. When 5 is subtracted from both sides we have 2y=0 which means y=0.
The solution is (5,0)
Directions for This Lesson:
Watch the video below and do the practice questions.
Required Video:
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