Can some explain how to make this equations

Question

I don't even know how my friends got the answers is : x = -10,-4;y = 4,2

 

Anyone can explain this?And i stuck with question

2 + 3y = 2,x^2+y^2+3xy=-4 , Tomorrow is the last days to sent the homework.

Answer 1

You have two equations:

 2 + 3 y = 2 ---> I am guessing you had it like  2 x + 3 y = 2 instead. 

x² + y² + 3 x y = -4

You can find the solution by using the substitution method. First, let us solve the first equation for x. 

2 x + 3 y = 2
2x = 2 - 3y
x = 1 - (3/2) y

Now let us plug in this result into the second one:

x² + y² + 3 x y = -4
Notice that x² + y² +2 xy can be written as (x+y)², therefore, we have:
(x+y)² + xy = -4
[1 - (3/2) y + y]² + (1 - (3/2) y) y = -4

[1 - (1/2) y]² + y - (3/2) y² = -4

1 - y + (1/4) y² + y - (3/2) y² = -4
-5/4 y² + 1 = -4
-5/4 y² = -5
y² = 4
y = -2 or y = 2
Correspondingly
x = 4 or x = -2

Thus you would find:

(4, -2) and (-2, 2)