Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 29 \
- 4 x + y ^ { 2 } = 17
\end{array}$$
A) $( 2,5 )$
B) $( 2,5 ) , ( 2 , - 5 )$
C) $( 2,5 ) , ( 2 , - 5 ) , ( - 6,5 ) , ( - 6 , - 5 )$
D) $( 2,5 ) , ( 2 , - 5 ) , ( - 2,5 ) , ( - 2 , - 5 )$

Question

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 29 \
- 4 x + y ^ { 2 } = 17
\end{array}$$
A) $( 2,5 )$
B) $( 2,5 ) , ( 2 , - 5 )$
C) $( 2,5 ) , ( 2 , - 5 ) , ( - 6,5 ) , ( - 6 , - 5 )$
D) $( 2,5 ) , ( 2 , - 5 ) , ( - 2,5 ) , ( - 2 , - 5 )$

Quizplus · Accepted Answer

The system of equations can be solved by substitution. Solving the second equation for $y^2$ and substituting into the first equation gives:$$x^2 + (17 + 4x) = 29$$$$x^2 + 4x - 12 = 0$$$$(x - 2)(x + 6) = 0$$$$x = 2, -6$$Substituting each value of $x$ back into the second equation gives:$$y^2 = 5, y = \pm 5$$Therefore, the solutions to the system of equations are $(2, 5)$ and $(2, -5)$.

Determine the Real Solutions to the System of Nonlinear Equations x2+y2=29−4x+y2=17\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 29 \\- 4 x + y ^ { 2 } = 17\end{array}x2+y2=29−4x+y2=17​

Determine the Real Solutions to the System of Nonlinear Equations $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 29 \\- 4 x + y ^ { 2 } = 17\end{array}$