Algebra Problem! Please Help Me! I Need This Answered Today!

Question

Solve the system:

x² + y² = 37

3x - 9 = y

There are two solutions: (x₁, y₁) (x₂, y₂).

Evaluate: x₁+y₁+x₂+y₂=

(A) 0

(B) (-21+2/3)

(C) (3+3/5)

(D) (7+3/7)

(E) None of the above

For this I got; (C) (3+3/5). Is this the correct answer?

Answer 1

Yes, you are correct.

You can also solve this the direct way by substituting y = 3x - 9 into the first equation, the result is a quadratic equation in x which factors cleanly. Then just take the two possible values for x, find the corresponding y's, and add the results.

Answer 2

Hello Jesset!

From this equation

3x - 9 = y

(3x - 9)² = y²

Replacing y² in x² + y² = 37

(3x - 9)² + x² = 37

9x² -54x + 81 + x² = 37

10x² -54x +44 = 0

From this equation, we have, x1 + x2 = 54/10 = 27/5 (the sum of the roots)

3x1 - 9 = y1

3x2 - 9 = y2 (summing these equations)

3*(x1 + x2) -18 = y1 + y2

Replacing (x1 + x2) by 27/5 :

3*(27/5) -18 = y1 + y2

81/5 - 90/5 = y1 + y2

y1 + y2 = -9/5

x1 + x2 + y1 + y2 = (x1 + x2) + (y1 + y2) = 27/5 - 9/5 = 18/5 = 3 + 3/5

Letter C, you are correct!

Feel free to send me any doubts related to Algebra, ok? Best regards!