Question

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?
StartLayout Enlarged left-brace 1st Row 5 x squared + 6 y squared = 50 2nd row negative 21 x squared minus 6 y squared = 10 EndLayout
StartLayout Enlarged left-brace 1st Row 5 x squared + 6 y squared = 50 2nd row negative 21 x squared minus 6 y squared = 30 EndLayout
StartLayout Enlarged left-brace 1st Row 35 x squared + 42 y squared = 250 2nd row negative 35 x squared minus 10 y squared = negative 50 EndLayout
StartLayout Enlarged left-brace 1st Row 35 x squared + 42 y squared = 350 2nd row negative 35 x squared minus 10 y squared = negative 50 EndLayout

Answer 1

The fourth system:

35x^2 + 42y^2 = 350
-35x^2 - 10y^2 = -50

Reason: multiply the first original equation 5x^2 + 6y^2 = 50 by 7 to get 35x^2 + 42y^2 = 350, and multiply the second 7x^2 + 2y^2 = 10 by -5 to get -35x^2 - 10y^2 = -50. Multiplying equations by nonzero scalars yields an equivalent system (same solution set).