Linear and Quadratic Equations

Question 1

Isolationg Varibale: Substitution Method

Answer 1

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

Question 2

Combination Method : Different sign

Answer 2

Add them: 
-2x+2y= 100
\+2x+2y= 100
-------------------
4y= 200

Question 3

Combination Method : Same sign

Answer 3

Subtract them 
-2x+2y= 100
\+2x+2y= 100
-------------------
-2x+2y= 100
-(+2x+2y= 100)

Question 4

Combination or Substitution:
2x+4y=50
14x+7y=10

Answer 4

Combination

Question 5

Combination or Substitution:
3y=12+6x
15y-20x=5.5

Answer 5

Substitution

Question 6

Combination or Substitution:
55x+10y= 101
2x+y = 76

Answer 6

Substitution

Question 7

Combination or Substitution:

7a+14b=28

Answer 7

Combination

Question 8

When to use a combination and when to use substitution:

-> Combination

Answer 8

When neither equation can be solved for one of the variables

Question 9

When to use a combination and when to use substitution:

-> Substitution

Answer 9

Use substitution when one equation can easily be solved for one of the variables

Question 10

Equation with Fractions

Answer 10

Find the LCM and solve it as you would with normal fractions

Question 11

Solving for one varibale interms of y : What is x interms of y

Answer 11

the only variblae in the answer will be is y

x= 4y+2

Question 12

When all the terms in an expression or equation have a common factor, the common factor can be

Answer 12

Factored out

• > 20rxy+20sxy=100
• -> r+s= 5

Question 13

Product of two integers: 2 possible way

Answer 13

1) both can be 1 (1*1)

2) both can be 1 (-1*-1)

Question 14

If two things multiply to zero, then aleast one of them must be equal to

Answer 14

0
a*b=0
–> either a is 0 or b is 0 or both are 0

Question 15

x(x+100)=0

Answer 15

x=0

x+10=0

Question 16

(x+y)^2

Answer 16

-> (x+y)(x+y)

= x^2+y^2+2xy

Question 17

(x-y)^2

Answer 17

• > (x-y)(x-y)

- > x^2+y^2-2xy

Question 18

(x+y)(x-y)

Answer 18

x^2-y^2

Question 19

x^2-1

Answer 19

(x-1)(x+1)

Question 20

4x^2-100

Answer 20

(2x-10)(2x+10)

Question 21

x^2y^2-16

Answer 21

(xy-4)(xy+4)

Question 22

1/36x^2-25

Answer 22

(1/6x-5)(1/6x+5)

Question 23

3^30-2^30

Answer 23

= (3^15)^2-(2^15)^2

= (3^15+2^15)(3^15-2^15)

Question 24

2^12-1

Answer 24

(2^6)^2-(1)^2= (2^6-1)(2^6+1)

Question 25

(x-y)/(x-y)

Answer 25

1

Question 26

(x-y)/(y-x)

Answer 26

-1

Question 27

Two equations that are same

Answer 27

x+y=2

10+10y=20

Question 28

Equation Trap #1: two equtions are the same

Answer 28

x+y=2

10x+10y=20

Question 29

Equation Trap #2: one equation is sufficient to determine the unique value

Answer 29

3.50s+2.50g= 35

Question 30

Do quadratic equation need to have 2 unique value

Answer 30

No - sometimes cannot have any real, sometimes have only one and can have two too

Question 31

When can you divide a varibale

Answer 31

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

Question 32

Before solving a quadratic equation

Answer 32

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