Solve the system of equation (only real solutions) by the elimination method. Check your solutions. x² + y^2 + 2x = 25
x² + 4y^2 + 3x = 32

9514 1404 393

  (-17/3, -√38/3), (-17/3, √38/3), (4, -1), (4, 1)

Step-by-step explanation:

We can subtract the second equation from 4 times the first to obtain a quadratic in x, with y eliminated.

  4(x² +y² +2x) -(x² +4y² +3x) = 4(25) -(32)

  3x² +5x -68 = 0 . . . . . simplify to standard form

  (3x +17)(x -4) = 0 . . . . . factor

  x = -17/3, +4 . . . . . . . . . solutions that make the factors zero

The corresponding values of y can be found from ...

  y = ±√(25 -x(2 +x)) . . . . solve the first equation for y

For x = -17/3, we get ...

  y = ±√(25 -(-17/3)(2 -17/3)) = ±√(38/9) = ±(√38)/3 ≈ ±2.05480

For x = 4, we get ...

  y = ±√(25 -4(2 +4)) = ±1

__

The solutions are ...

  (-17/3, -√38/3), (-17/3, √38/3), (4, -1), (4, 1)

is only a line? i think so