9514 1404 393
Answer:
(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)
