Find all real solutions to the system of equations using the addition method.
-$\begin{aligned}
x ^ { 2 } - 3 y ^ { 2 } & = 1 \
4 x ^ { 2 } + 3 y ^ { 2 } & = 19
\end{aligned}$
A)(2, 1), (-2, -1)
B)(2, 1), (2, -1), (-2, 1), (-2, -1)
C)(1, 2), (-1, 2), (1, -2), (-1, -2)
D)(-1, 2), (1, -2)

Question

Quizplus · Accepted Answer

By adding the two equations, we eliminate $y^2$ and get $5x^2 = 20$, leading to $x^2 = 4$, so $x = \pm 2$. Substituting $x$ back into one of the original equations allows us to solve for $y$, yielding $y = \pm 1$. Thus, the solutions are $(2, 1)$, $(2, -1)$, $(-2, 1)$, and $(-2, -1)$.

Find All Real Solutions to the System of Equations Using x2−3y2=14x2+3y2=19\begin{aligned}x ^ { 2 } - 3 y ^ { 2 } & = 1 \\4 x ^ { 2 } + 3 y ^ { 2 } & = 19\end{aligned}x2−3y24x2+3y2​=1=19​

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