Question

drag the solution(s) of the system into the bin.
x = \frac{1}{18}y^2
y^2 = -18x + 72
keyboard help
solutions
no solutions \\(\left(\frac{72}{17}, \frac{36\sqrt{17}}{17}\
ight)\\) \\(\left(\frac{72}{17}, -\frac{36\sqrt{17}}{17}\
ight)\\) \\(\left(-\frac{36\sqrt{17}}{17}, \frac{72}{17}\
ight)\\) \\(\left(\frac{36\sqrt{17}}{17}, \frac{72}{17}\
ight)\\)
(2, 6) (2, -6) (6, 2) (-6, 2)

Explanation:

Step1: Sustituir \( y^2 \) en la segunda ecuación

De la primera ecuación \( x = \frac{1}{18}y^2 \), despejamos \( y^2 = 18x \). Sustituimos en la segunda ecuación \( y^2 = -18x + 72 \):
$$18x = -18x + 72$$

Step2: Resolver para \( x \)

Sumamos \( 18x \) a ambos lados:
$$36x = 72$$
Dividimos por 36:
$$x = 2$$

Step3: Encontrar \( y \)

Sustituimos \( x = 2 \) en \( y^2 = 18x \):
$$y^2 = 18(2) = 36$$
Tomamos raíces: \( y = 6 \) o \( y = -6 \)

Step4: Verificar soluciones

Comprobamos \( (2, 6) \): \( x = \frac{1}{18}(6)^2 = \frac{36}{18} = 2 \), \( y^2 = -18(2) + 72 = 36 \), correcto.
Comprobamos \( (2, -6) \): \( x = \frac{1}{18}(-6)^2 = 2 \), \( y^2 = -18(2) + 72 = 36 \), correcto.

Answer:

(2, 6), (2, -6)