morenikejasmine morenikejasmine
  • 10-03-2022
  • Mathematics
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x²-6xy+11y²=3a²
x²-2xy-3y²=5a²​

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chaneldemoure
chaneldemoure chaneldemoure
  • 10-03-2022
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.
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