Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l }
x ^ { 2 } + y ^ { 2 } = 64 \
\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1
\end{array} \right.$$
A) x = 0, y= -8; x = 0, y = 8
B) x = -8, y= 0; x = 8, y = 0
C) x = 0, y= -3; x = 0, y = 3
D) inconsistent

Question

Solve the system of equations using elimination.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 64 \
\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1
\end{array} \right.$$
A) x = 0, y= -8; x = 0, y = 8
B) x = -8, y= 0; x = 8, y = 0
C) x = 0, y= -3; x = 0, y = 3
D) inconsistent

Quizplus · Accepted Answer

The first equation represents a circle with radius 8 centered at the origin, and the second equation represents an ellipse. By multiplying the second equation by 64*9=576, we get $x^2 + 9y^2 = 576$. Substituting $x^2 + y^2 = 64$ into this equation, we can solve for $y^2$ and $x^2$, finding that the solutions are where either $x = 8, x = -8$ and $y = 0$, which corresponds to the points where the circle and ellipse intersect on the x-axis.

Solve the System of Equations Using Elimination {x2+y2=64x264+y29=1\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 64 \\\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1\end{array} \right.{x2+y2=6464x2​+9y2​=1​

Solve the System of Equations Using Elimination $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 64 \\\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1\end{array} \right.$