# Solving Systems of Equations

## Introducing Solving Systems

When solving just one equation you're trying to find X. When solving a systems of equations you're trying to find the X and Y. A system of equations will always have two equations.

Their are several ways of solving systems of equations. Graphing, Substitution, and Elimination. My preferred way to solve equations is graphing.

Graphing is when you put the two equations on a graph to find the point of intersection.

Elimination is canceling out everything to find the X and Y values.

Substitution is taking one equation and plugging it in the other to find the X value, then take that and plug it into the other equation to find the Y value

Any system can be solved by graphing. For example: plug in y=4x+7 and y=2/3x-2 in Y= on your calculator then press 2nd, trace, go down to intersect and press enter 3 times. The intersecting points are (-2.7,-3.8). This is sometimes the easiest way to solve equations because its strait forward.

REMEMBER: Sometimes you have to write the equations out before you can solve them.

Equations can also be solved by elimination by canceling out everything to find the X and Y points.

For example: if you have the two equations 6x+3y=12 and -6x+y=-20 you would subtract them. Also, its a lot easier to solve by elimination if either the X or Y values cancel out.

6x+3y=12

-6x+y=-20

4y=-8

4

Y=-2

The X cancels out, you have 4 Y's and a -8. Divide them by 4 and Y= -2. Then plug in the Y value in one of the original equations to solve for X. The Y becomes a -6 and the equation is 6x-6=12. Add 6 to both sides of the equals sign so its 6x=18. After that divide by 6 and X=3.

6x+3(-2)=12

6x-6=12

6x=18

6

X=3

Another way to solve an equation is by substitution. For example: if you had the two equations 6x+8y=30 and y=-4x+20 you would plug in the second equation into the first equation's Y intercept and solve for X. x=5

6x+8(-4x+20)=30

6x-32x+160=30

-26x+160=30

-26x=-130

-26

X=5

Then plug in the X value into the second equation to find the Y value and y=0.

y=-4(5)+20

y=-20+20

y=0