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.