Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 25 \
x + y = 7
\end{array}$$
A)(4, -3), (3, -4)
B)(4, 3), (3, 4)
C)(-4, 3), (-3, 4)
D)(-4, -3), (-3, -4)

Question

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
x + y = 7
\end{array}$$
A)(4, -3), (3, -4)
B)(4, 3), (3, 4)
C)(-4, 3), (-3, 4)
D)(-4, -3), (-3, -4)

Quizplus · Accepted Answer

From the second equation, $y = 7 - x$. Substituting this into the first equation gives $x^2 + (7 - x)^2 = 25$. Simplifying, we get $2x^2 - 14x + 24 = 0$, which simplifies to $x^2 - 7x + 12 = 0$. Factoring, we get $(x - 3)(x - 4) = 0$, so $x = 3$ or $x = 4$. Substituting these values back into $y = 7 - x$, we find the pairs (3, 4) and (4, 3), which correspond to choice B.

Determine the Real Solutions to the System of Nonlinear Equations x2+y2=25x+y=7\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\x + y = 7\end{array}x2+y2=25x+y=7​

Determine the Real Solutions to the System of Nonlinear Equations $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 25 \\x + y = 7\end{array}$