What is the method for working out quadratic simultaneous equations?
X squared * Y squared =5
Y-X=3
I only know how to work these out through trial and error
Thanks!
You can attempt to solve any system of simultaneous equations by the method of substitution. Example.
\(\displaystyle x^2 + y - z = 41\).
\(\displaystyle x + y + z = 7\).
\(\displaystyle 5x + 3y + 4z = 18.\)
\(\displaystyle z = \dfrac{1}{4} * (18 - 5x - 3y) \ \because \ 5x + 3y + 4z = 18.\)
\(\displaystyle \therefore x + y + z = 7 \implies 28 = 4x + 4y + 18 - 5x - 3y \implies y = 10 + x.\)
\(\displaystyle \text {And } x^2 + y - z = 41 \implies 4x^2 + 4y - (18 - 5x - 3y) = 164 \implies\)
\(\displaystyle 4x^2 + 7y + 5x - 18 = 4x^2 + 7(10 + x) + 5x - 18 = 164 \implies\)
\(\displaystyle 4x^2 + 12x - 112 = 0 \implies x^2 + 3x - 28 = 0 \implies (x + 7)(x - 4) = 0 \implies\)
\(\displaystyle x = 4 \text { or } x = -\ 7.\)
\(\displaystyle x = 4 \implies y = 14 \implies z = \dfrac{1}{4} * (18 - 20 - 42) = -\ 11.\)
\(\displaystyle x = -\ 7 \implies y = 3 \implies z = \dfrac{1}{4} * (18 + 35 - 9) = 11.\)
It must be admitted, however, the systems of non-linear equations can get very ugly even with substitution.