# Solving Systems of Equations!

### Math Models- McKenna Robinson

## What is "Solving Systems of Equations"?

**If you solving for equations, your wanting to find X.**

If you are solving systems, then your wanting to find X and Y.

A system of equations have more than one equation, such as:

7x+2y=10

-7x+y=-16

Their are many ways of **Solving Systems by** **Graphing and Point of intersection**

Solving by graphing mean each equations will find the point of intersection on a graph.

Example:

**y=1/4x-2**

**y=-4x+2**

You can do this by going to **(Y=)** on your graphing calculator and putting in the problems in **Y1** and **Y2**, hitting **graph**, then **second**, **trace**, **(5)** intersect, then **enter 2x **then you get your X and Y! :)

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Another way of solving systems is **Solving by Substitution**!

Example:

**2x+3y=4**

**y=5x-27**

**2x+3(5x-27)=4**

**Multiply 3 times 5x and -27**

**2x+15x-81=4**

**Then add the X's**

**17x-81=4**

**Then add 81 to 4 **

**17x=85**

**Then divide 85 by 17**

**x=-5**

** **:D!!!

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You also have **Solving by Elimination**!

Solving by Elimination is similar to solving by substitution but your finding X and Y.

Example:

**2x+3y=20**

**-2x+y=4**

Add them together..

** 2x+3y=20**

**+ -2x+y=4 **

** = 0+4y=24**

**4y=24 Divid 24 by four and you get...**

** y=6**

Now we have to find x...write the problem down again, but in the **Y place**, put **6**!

example:

**-2x+6=4**

Then you **solve** for **X** and you get **1=x**

Yay, you found out how to find X and Y! :D

Lets go over the things you learned!

**Systems of Equations**: Solving by Elimination is similar to solving by substitution but your finding X and Y

**Point of Intersection**: finding the point that one equation and another intersect one another on a graph and getting the coordinates x and y.

**Solving by Graphing**:Solving by graphing mean each equations will find the point of intersection on a graph

**Solving by Substitution**: Systems of equations can be solved by substitution, finding x and y

**Solve by elimination**: Solving by Elimination is similar to solving by substitution but your finding X and Y.