Question

solve the following system.
$4x^{2}+9y^{2}=72$
$x^{2}-y^{2}=5$
list your answers in numerical order by the $x$-value and then the $y$-value. remember to include the commas.
the solutions are ( ), ( ), ( ), and ( )

Explanation:

Step1: Isolate $x^2$ from second equation

$x^2 = y^2 + 5$

Step2: Substitute $x^2$ into first equation

$4(y^2 + 5) + 9y^2 = 72$

Step3: Expand and simplify the equation

$4y^2 + 20 + 9y^2 = 72$
$13y^2 = 52$

Step4: Solve for $y^2$ and $y$

$y^2 = 4$
$y = 2, -2$

Step5: Find $x^2$ and $x$ for $y=2$

$x^2 = 2^2 + 5 = 9$
$x = 3, -3$

Step6: Find $x^2$ and $x$ for $y=-2$

$x^2 = (-2)^2 + 5 = 9$
$x = 3, -3$

Step7: Order pairs by $x$, then $y$

Sort $(-3,-2), (-3,2), (3,-2), (3,2)$

Answer:

$(-3, -2)$, $(-3, 2)$, $(3, -2)$, $(3, 2)$