Find all real solutions to the system of equations using the substitution method.
-$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 41 \
x + y = 9
\end{array}$
A)(-5, 4), (-4, 5)
B)(5, 4), (4, 5)
C)(5, -4), (4, -5)
D)(-5, -4), (-4, -5)

Question

Find all real solutions to the system of equations using the substitution method.
-$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 41 \
x + y = 9
\end{array}$
A)(-5, 4), (-4, 5)
B)(5, 4), (4, 5)
C)(5, -4), (4, -5)
D)(-5, -4), (-4, -5)

Quizplus · Accepted Answer

From the second equation, $y = 9 - x$. Substituting this into the first equation gives $x^2 + (9 - x)^2 = 41$. Solving this equation for $x$ yields $x = 5$ or $x = 4$. Substituting these values back into $y = 9 - x$ gives the pairs (5, 4) and (4, 5).

Find All Real Solutions to the System of Equations Using x2+y2=41x+y=9\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 41 \\x + y = 9\end{array}x2+y2=41x+y=9​

Find All Real Solutions to the System of Equations Using $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 41 \\x + y = 9\end{array}$