Answer:
(0, - 1 ) , (-
,
)
Explanation:
given the 2 equations to solve simultaneously
x² + y² = 1 → (1)
3x + y = - 1 ( subtract 3x from both sides )
y = - 1 - 3x → (2)
substitute y = - 1 - 3x into (1)
x² + (- 1 - 3x)² = 1 ← expand parenthesis using FOIL
x² + 1 + 6x + 9x² = 1
10x² + 6x + 1 = 1 ( subtract 1 from both sides )
10x² + 6x = 0 ← factor out 2x from each term on the left side
2x(5x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
5x + 3 = 0 ( subtract 3 from both sides )
5x = - 3 ( divide both sides by 5 )
x = -

substitute these values of x into (2) for corresponding y values
x = 0 : y = - 1 - 3(0) = - 1 - 0 = - 1 ⇒ (0, - 1 )
x = -
: y = - 1 - 3(-
) = -
+
=
⇒ (-
,
)
solutions are (0, - 1 ) and (-
,
)