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Graphing System of Equations in Geometry and Beyond 

Have you ever been confused by the process of graphing a system of equations? Geometry and other math classes often require us to graph equations, and it can be daunting if you don’t understand the process. But never fear - this blog post will demystify the process and give you an overview of how to graph a system of equations. 

What is a System of Equations? 

A system is made up of two or more equations that have the same variables. To solve for these variables, we need to use either substitution or elimination. Depending on what type of system it is, you may be able to do one or both methods. 

When using substitution, we take an equation and substitute it into another equation. This means that whatever value we get from one equation will become a part of another equation. For example, let’s say we have the following system: y = x + 2  and  y = 3x - 2  We can substitute 3x - 2 into y = x + 2 to get 3x - 2 = x +2, which simplifies to x = 4. Now that we know what x equals, we can go back and plug in 4 for x in either equation to find out what y equals. In this case, y would equal 6. 

The other method is elimination, which involves adding or subtracting two equations together so that one variable cancels out. Let’s look at our previous example again:  y = x + 2  and  y = 3x -2  First, let’s add these two equations together so that one variable (y) cancels out: x + 2 + 3x -2= 0  This simplifies to 4x= 0 so x must equal 0 in order for this equation to hold true. Then all we need to do is plug 0 back into either equation in order to find out what y equals; in this case, it would be 2! 

Graphing System of Equations After solving for our variables using substitution or elimination , we now have all the information we need in order draw our graph! All we have to do is plot our points on a coordinate plane – for example if x=4 & y=6 then (4,6) would be our point – then draw lines connecting those points until they create a shape on the graph. That shape will represent the solution set for your system! It may feel like a lot at first but with practice graphing systems becomes much easier – soon enough you'll be making graphs without even thinking about it! 

 

Conclusion:

As you can see from this post, graphing systems doesn't have to be intimidating! By understanding what makes up a system and how each method works, you'll start feeling more comfortable with graphing systems no matter what class you're taking! With practice under your belt soon make graphing systems second nature! Good luck!

FAQ

What is a graphing method system of equations?

A graphing system of equations is when two or more equations have the same variables, and you need to use substitution or elimination in order to solve for those variables. Then, after solving for the variables, you can plot your points on a coordinate plane and draw lines connecting them until they create a shape that represents the solution set for your system.

What is system of equations in geometry?

Systems of equations in geometry are when two or more equations have the same variables and you need to use substitution or elimination in order to solve for those variables. These equations can be linear, quadratic, cubic, etc., and once solved, can often help us find the area, volume, or perimeter of a given shape.

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