two or more equations with the same variables
System of equations
the order of adding does not change the sum or product
a specific relationship in which there is a constant ratio between all ordered pairs
Direct variation
2^5
2*2*2*2*2
32
4(x+3)>-24
4x+27>-24
4x/4>-36/4
x>-9
A method of solving systems if equations by substituting one equation into the other
Substitution method
Grouping numbers differently does not change the sum or product
Associative
Direct variation equation is
y=kx
2^2
2*2
4
x-3(x+2)>4
x-3x-6>4
-2x-6>4
-2x/-2>10/-2
x<-5
A method for solving systems of equations by combining the equations to eliminate one variable
Elimination method
Identity
Specific relationship in which there is a constant product ( x*y) between all ordered pairs
inverse variation
2^2/
2^5
2*2/
2*2*2*2*2
1/
2^3
7x-2(x-4)<-2
7x-2x+8<-2
5x+8-8<-2-8
5x/x<-10/5
x<-2
4x+9y=5
-4x+7y=11
Solve
(-1,1)
Multiplication Property of zero or
the zero property
Inverse variation equations
y= k/x
17x-25x
-8x
-8(x-1)-x<-28
-8x+8-x<-28
-9x+8<-28
-9x<-36
x>4
2x + y= -10
-y= 2x+10
solve
0=0
a(b+c)=a*b+a*c
Distributive property
a bell curve that shows how data is distributed about the mean
Normal distribution
-23y^2+6y^2
-17y^2
2x-1<5x+20
-1-20<3x+20-20
-21/3<3x/3
-7<x