The system of equations can be rewritten as follows:
1) x - y = 22) y^2 - 3 = 2xy3) 3xy + x = -24) 6xy + y = -2
We can solve this system of equations by manipulating them to isolate one variable in terms of another. Let's start with equation 1):
x = y + 2
Now, we can substitute this expression for x into the other equations to simplify:
2) y^2 - 3 = 2(y + 2)yy^2 - 3 = 2y^2 + 4y0 = y^2 + 4y + 30 = (y + 1)(y + 3)y = -1 or y = -3
Now we can find the corresponding values of x by plugging y back into x = y + 2:
For y = -1, x = -1 + 2 = 1For y = -3, x = -3 + 2 = -1
So, there are two possible solutions to this system of equations:1) x = 1 and y = -12) x = -1 and y = -3
The system of equations can be rewritten as follows:
1) x - y = 2
2) y^2 - 3 = 2xy
3) 3xy + x = -2
4) 6xy + y = -2
We can solve this system of equations by manipulating them to isolate one variable in terms of another. Let's start with equation 1):
x = y + 2
Now, we can substitute this expression for x into the other equations to simplify:
2) y^2 - 3 = 2(y + 2)y
y^2 - 3 = 2y^2 + 4y
0 = y^2 + 4y + 3
0 = (y + 1)(y + 3)
y = -1 or y = -3
Now we can find the corresponding values of x by plugging y back into x = y + 2:
For y = -1, x = -1 + 2 = 1
For y = -3, x = -3 + 2 = -1
So, there are two possible solutions to this system of equations:
1) x = 1 and y = -1
2) x = -1 and y = -3