SOLUTION: What is a system equation?

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Question 709958: What is a system equation?
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

A system of equations is a collection of two or more equations with a same set of unknowns.
In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.
The equations in the system can be linear or non-linear.

Example of an algebraic statement of the same system of the equations:
3x-2y=1.....eq.1
x%2By=3.....eq.2
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A system of linear equations can be solved four different ways:

Substitution
Gaussian+Elimination
Matrices
Graphing
let's use Graphing to solve the system above:

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


3x-2y=1

1x%2By=3





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


3x-2y=1 Start with the given equation



-2y=1-3x Subtract 3+x from both sides



-2y=-3x%2B1 Rearrange the equation



y=%28-3x%2B1%29%2F%28-2%29 Divide both sides by -2



y=%28-3%2F-2%29x%2B%281%29%2F%28-2%29 Break up the fraction



y=%283%2F2%29x-1%2F2 Reduce



Now lets graph y=%283%2F2%29x-1%2F2 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F2%29x-1%2F2%29+ Graph of y=%283%2F2%29x-1%2F2




So let's solve for y on the second equation


1x%2By=3 Start with the given equation



1y=3-x Subtract +x from both sides



1y=-x%2B3 Rearrange the equation



y=%28-x%2B3%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%283%29%2F%281%29 Break up the fraction



y=-x%2B3 Reduce





Now lets add the graph of y=-x%2B3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%283%2F2%29x-1%2F2%2C-x%2B3%29+ Graph of y=%283%2F2%29x-1%2F2(red) and y=-x%2B3(green)


From the graph, we can see that the two lines intersect at the point (7%2F5,8%2F5) (note: you might have to adjust the window to see the intersection)