Can someone help and explain it step by step, please!!

9514 1404 393

  (x, y) = {(-32/17, 49/17), (-2, 1)}

Step-by-step explanation:

I find a graphing calculator to be quite helpful in finding the solutions.

  (x, y) = {(-1.882, 2.882), (-2, 1)}

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For this sort of system of equations, substitution works nicely as a solution method.

The first equation tells us ...

  y = 1 - x

Using that in the second equation, we get ...

  16x² +(1 -x)² = 65

  16x² +1 -2x +x² = 65 . . . . . eliminate parentheses

  17x² -2x -64 = 0 . . . . . . . . collect terms, subtract 65

  (x -2)(17x +32) = 0 . . . . . . . factor

Solutions are the values of x that make the factors zero: x = 2, x = -32/17.

The corresponding y-values are ...

  for x=2, y = 1-2 = -1

  for x=-32/17, y = 1-(-32/17) = 49/17

The solutions are ...

  (x, y) = (2, -1)  or  (-32/17, 49/17)