Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
$\begin{array} { l }
y = \sqrt [ 4 ] { 2 x + 9 } \
x ^ { 2 } + y ^ { 2 } = 5.7
\end{array}$
A) {(-1.84,1.52),(1.50,1.86)}
B) {(-1.84,-1.52),(1.50,-1.86)}
C) {(-1.50,-1.86),(1.84,-1.52)}
D) {(-1.50,1.86),(1.84,1.52)}

Question

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
$\begin{array} { l } 
y = \sqrt [ 4 ] { 2 x + 9 } \
x ^ { 2 } + y ^ { 2 } = 5.7
\end{array}$
A) {(-1.84,1.52),(1.50,1.86)} 
B) {(-1.84,-1.52),(1.50,-1.86)} 
C) {(-1.50,-1.86),(1.84,-1.52)} 
D) {(-1.50,1.86),(1.84,1.52)}

Quizplus · Accepted Answer

Solving the system of equations using a graphing calculator involves plotting both equations and finding their points of intersection. The first equation, $y = \sqrt[4]{2x + 9}$, represents a function that only produces positive y-values for the given domain of x, since the fourth root of any real number is either positive or zero. The second equation, $x^2 + y^2 = 5.7$, represents a circle centered at the origin with a radius squared of 5.7. The intersection points of these two graphs give the solutions to the system. The correct answer, therefore, includes points with both positive and negative x-values but only positive y-values, as indicated by the graph of the first equation. This matches option A, which provides two points of intersection with positive y-coordinates, consistent with the output of the fourth root function in the first equation.

Use a Graphing Calculator to Solve the Nonlinear System y=2x+94x2+y2=5.7\begin{array} { l } y = \sqrt [ 4 ] { 2 x + 9 } \\x ^ { 2 } + y ^ { 2 } = 5.7\end{array}y=42x+9​x2+y2=5.7​

Use a Graphing Calculator to Solve the Nonlinear System $\begin{array} { l } y = \sqrt [ 4 ] { 2 x + 9 } \\x ^ { 2 } + y ^ { 2 } = 5.7\end{array}$