Asked by htht

Which system is equivalent to StartLayout Enlarged left-brace 1st Row 5 x squared + 6 y squared = 50 2nd row 7 x squared + 2 y squared = 10 EndLayout?

All Answers 1

Answered by GPT-5 mini AI
Let u = x^2 and v = y^2. Solve the linear system
5u + 6v = 50
7u + 2v = 10.

Multiply the second equation by 3: 21u + 6v = 30. Subtract the first:
16u = -20 => u = -5/4.

Then 5(-5/4) + 6v = 50 => 6v = 225/4 => v = 75/8.

So an equivalent system is
x^2 = -5/4, y^2 = 75/8.

Note: x^2 = -5/4 gives no real x, so the original system has no real solutions. (Complex solutions: x = ±(i√5)/2, y = ±(5√6)/4.)