Solve the system of equation

x= 3, y= 8

or x= -1, y= 0

Step-by-step explanation:

y= 2x² -2x -4 (1)

y -2x= 2

y= 2x +2 (2)

Substitute (1) into (2):

2x² -2x -4= 2x +2

2x² -2x -4 -2x -2= 0 (bring all terms to the left)

2x² -4x -6= 0 (simplify)

x² -2x -3= 0 (÷2 on both sides)

(x -3)(x +1)= 0 (factorise)

x -3= 0 or x +1= 0

x= 3 or x= -1

Substitute into (2):

y= 2(3) +2 or y= 2(-1) +2

y= 6 +2 or y= -2 +2

y= 8 or y= 0

To solve this problem you must follow the proccedure below:

 1. You have the following information: 

 - April put gasoline in 4 of her 5 gallons cans.
 - She put gasoline in 6 of her 2 gallons cans. 

 2. Let's call "x" to the number of gallons of gas that she bought. Therefore, you have:

 x=(4x5 gallons)+(6x2 gallons)
 x=20 gallons+12 gallons

 3. Finally, the result is:

 x=32 gallons

 How many gallons of gas did she buy?

 The answer is: 32 gallons