Linear and Quadratic Equations Flashcards
Isolationg Varibale: Substitution Method
When you are using substituion, try to isolate the one that is less complex
- > 4y= 5+b
- > b=4y-5 —> simpler one so substitute it here
Combination Method : Different sign
Add them: -2x+2y= 100 \+2x+2y= 100 ------------------- 4y= 200
Combination Method : Same sign
Subtract them -2x+2y= 100 \+2x+2y= 100 ------------------- -2x+2y= 100 -(+2x+2y= 100)
Combination or Substitution:
2x+4y=50
14x+7y=10
Combination
Combination or Substitution:
3y=12+6x
15y-20x=5.5
Substitution
Combination or Substitution:
55x+10y= 101
2x+y = 76
Substitution
Combination or Substitution:
7a+14b=28
Combination
When to use a combination and when to use substitution:
-> Combination
When neither equation can be solved for one of the variables
When to use a combination and when to use substitution:
-> Substitution
Use substitution when one equation can easily be solved for one of the variables
Equation with Fractions
Find the LCM and solve it as you would with normal fractions
Solving for one varibale interms of y : What is x interms of y
the only variblae in the answer will be is y
x= 4y+2
When all the terms in an expression or equation have a common factor, the common factor can be
Factored out
- > 20rxy+20sxy=100
- -> r+s= 5
Product of two integers: 2 possible way
1) both can be 1 (1*1)
2) both can be 1 (-1*-1)
If two things multiply to zero, then aleast one of them must be equal to
0
a*b=0
–> either a is 0 or b is 0 or both are 0
x(x+100)=0
x=0
x+10=0
(x+y)^2
-> (x+y)(x+y)
= x^2+y^2+2xy
(x-y)^2
- > (x-y)(x-y)
- > x^2+y^2-2xy
(x+y)(x-y)
x^2-y^2
x^2-1
(x-1)(x+1)
4x^2-100
(2x-10)(2x+10)
x^2y^2-16
(xy-4)(xy+4)
1/36x^2-25
(1/6x-5)(1/6x+5)
3^30-2^30
= (3^15)^2-(2^15)^2
= (3^15+2^15)(3^15-2^15)
2^12-1
(2^6)^2-(1)^2= (2^6-1)(2^6+1)
(x-y)/(x-y)
1
(x-y)/(y-x)
-1
Two equations that are same
x+y=2
10+10y=20
Equation Trap #1: two equtions are the same
x+y=2
10x+10y=20
Equation Trap #2: one equation is sufficient to determine the unique value
3.50s+2.50g= 35
Do quadratic equation need to have 2 unique value
No - sometimes cannot have any real, sometimes have only one and can have two too
When can you divide a varibale
Only when you know that the variable is not equal to 0
-> x^2=100x
you can’t cancel the x’s out
-> x= 0, x-100=0
Before solving a quadratic equation
you have to move everything to one side i.e (x+3)(x+2)=12 = x^2+5+6-12=0 i.e x^2(x-5)=9(x-5) = (x-3)(x+3)(x+5)=0
