Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
-$x ^ { 2 } + y ^ { 2 } = 25$ $x - y = 1$
A) $\{ ( - 4 , - 3 ) , ( - 3 , - 4 ) \}$
B) $\{ ( 4,3 ) , ( - 3 , - 4 ) \}$
C) $\{ ( 4 , - 3 ) , ( 3 , - 4 ) \}$
D) $\{ ( - 4,3 ) , ( - 3,4 ) \}$

Question

Quizplus · Accepted Answer

To solve the system, substitute $x = y + 1$ into $x^2 + y^2 = 25$. This gives $(y + 1)^2 + y^2 = 25$, which simplifies to $2y^2 + 2y - 24 = 0$. Factoring or using the quadratic formula yields $y = 3$ or $y = -4$. Substituting these values back into $x = y + 1$ gives $x = 4$ when $y = 3$, and $x = -3$ when $y = -4$, resulting in the solutions $(4,3)$ and $(-3,-4)$.

Give All Solutions of the Nonlinear System of Equations, Including x2+y2=25x ^ { 2 } + y ^ { 2 } = 25x2+y2=25

Give All Solutions of the Nonlinear System of Equations, Including $x ^ { 2 } + y ^ { 2 } = 25$