Q: Given the simultaneous equations x²-6xy+11y²=3a², x²-2xy-3y²=5a²,derive an equation in x and y only, and hence solve the equations for x and y in terms of a.
Multiply the first equation by 5, the second by 3, and get 15^2 on both sides.
That means 5^2–30+55^2=3^2–6+9^2
which simplifies to:
^2–12+23^2=0
So,
=3±√ 13
Substitute each solution into either equation to get ^2 in terms of ^2.
and solve, then get , You should get either 0, 2 or 4 solutions.