m^2-3mn+n^2+1=0
3m^2-mn+3n^2=13
What are the solutions?
Thanks
I just figured this one out actually, thanks though!
To find the solutions to the given system of equations, we can use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other.
Let's solve the first equation for n:
m^2 - 3mn + n^2 + 1 = 0
Rearranging the equation, we get:
n^2 - 3mn + m^2 + 1 = 0
n^2 - (3m)n + (m^2 + 1) = 0
Step 2: Substitute the expression for n into the second equation.
Now substitute the expression we obtained for n in terms of m into the second equation:
3m^2 - mn + 3n^2 = 13
3m^2 - m(3m) + 3(m^2 + 1) = 13
3m^2 - 3m^2 + 3 + 3m^2 = 13
3 = 13
This is not a valid equation, as it is contradictory. Therefore, there are no solutions to the given system of equations.
In summary, there are no solutions to the system of equations.