Question

find the solution set for the system by graphing both of the systems equations in the same rectangular coordinate system and finding points of intersection. check all solutions in both equations.
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$$\begin{cases}\\frac{x^2}{4} + \\frac{y^2}{40} = 1 \\\\ x = -2\\end{cases}$$

choose the correct graph of the system below.
a. graph
b. graph
c. graph
d. graph

select the correct choice below and, if necessary, fill in the answer box to complete your answer.
\bigcirc a. the solution set is \boxed{}. (simplify your answer. type an ordered pair. use a comma to separate answers as needed.)
\bigcirc b. there is no solution.

Explanation:

Step1: Substitute \( x = -2 \) into the ellipse equation

The ellipse equation is \( \frac{x^2}{4} + \frac{y^2}{49} = 1 \). Substitute \( x = -2 \):
\( \frac{(-2)^2}{4} + \frac{y^2}{49} = 1 \)
Simplify \( \frac{4}{4} = 1 \), so \( 1 + \frac{y^2}{49} = 1 \).

Step2: Solve for \( y \)

Subtract 1 from both sides: \( \frac{y^2}{49} = 0 \).
Multiply both sides by 49: \( y^2 = 0 \), so \( y = 0 \).

Answer:

A. The solution set is \((-2, 0)\)