Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l }
y = - x ^ { 2 } + 3 \
x ^ { 2 } + y ^ { 2 } = 5
\end{array} \right.$$
A) $x = 2 , y = - 1 ; x = 1 , y = 2 ; x = - 1 , y = 2 ; x = - 2 , y = - 1$
B) $x = 1 , y = 4 ; x = 4 , y = 19$
C) $x = 1 , y = 2 ; x = - 1 , y = 2$
D) $x = 2 , y = - 1 ; x = - 2 , y = - 1$

Question

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
y = - x ^ { 2 } + 3 \
x ^ { 2 } + y ^ { 2 } = 5
\end{array} \right.$$
A) $x = 2 , y = - 1 ; x = 1 , y = 2 ; x = - 1 , y = 2 ; x = - 2 , y = - 1$
B) $x = 1 , y = 4 ; x = 4 , y = 19$
C) $x = 1 , y = 2 ; x = - 1 , y = 2$
D) $x = 2 , y = - 1 ; x = - 2 , y = - 1$

Quizplus · Accepted Answer

Substitute $y = -x^2 + 3$ into the second equation to get $x^2 + (-x^2 + 3)^2 = 5$. Solve for $x$ and $y$ to find the solutions listed in option A.

Solve the System of Equations Using Substitution {y=−x2+3x2+y2=5\left\{ \begin{array} { l } y = - x ^ { 2 } + 3 \\x ^ { 2 } + y ^ { 2 } = 5\end{array} \right.{y=−x2+3x2+y2=5​

Solve the System of Equations Using Substitution $\left\{ \begin{array} { l } y = - x ^ { 2 } + 3 \\x ^ { 2 } + y ^ { 2 } = 5\end{array} \right.$