Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 4 \
x + y = 2
\end{array} \right.$$
A) x = 0, y = 0; x = 2, y = -2
B) x = 0, y = -2; x = -2, y = 0
C) x = 2, y = -2; x = -2, y = -2
D) x = 0, y = 2; x = 2, y = 0

Question

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 4 \
x + y = 2
\end{array} \right.$$
A) x = 0, y = 0; x = 2, y = -2
B) x = 0, y = -2; x = -2, y = 0
C) x = 2, y = -2; x = -2, y = -2
D) x = 0, y = 2; x = 2, y = 0

Quizplus · Accepted Answer

From the second equation, $y = 2 - x$. Substituting this into the first equation gives $x^2 + (2-x)^2 = 4$. Simplifying, we get $2x^2 - 4x + 4 = 4$, which simplifies further to $2x^2 - 4x = 0$, or $x(x - 2) = 0$. Thus, $x = 0$ or $x = 2$. Substituting these values back into $y = 2 - x$, we find the corresponding $y$ values, leading to the solutions $x = 0, y = 2$ and $x = 2, y = 0$.

Solve the System of Equations Using Substitution {x2+y2=4x+y=2\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 4 \\x + y = 2\end{array} \right.{x2+y2=4x+y=2​

Solve the System of Equations Using Substitution $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 4 \\x + y = 2\end{array} \right.$