Question

to solve the system of equations below, grace isolated the variable ( y ) in the first equation and then substituted into the second equation. what was the resulting equation?
\begin{cases}4y = 8x \dfrac{x^2}{25} - dfrac{y^2}{49} = 1end{cases}

a. ( dfrac{x^2}{25} - dfrac{4y^2}{49} = 1 )

b. ( dfrac{x^2}{25} - dfrac{2x^2}{49} = 1 )

c. ( dfrac{x^2}{25} - dfrac{2y^2}{49} = 1 )

d. ( dfrac{x^2}{25} - dfrac{4x^2}{49} = 1 )

Explanation:

Step1: Isolate $y$ from first equation

Divide both sides of $4y=8x$ by 4:
$y = 2x$
Square both sides:
$y^2 = 4x^2$

Step2: Substitute $y^2$ into second equation

Replace $y^2$ with $4x^2$ in $\frac{x^2}{25}-\frac{y^2}{49}=1$:
$\frac{x^2}{25}-\frac{4x^2}{49}=1$

Answer:

D. $\frac{x^2}{25}-\frac{4x^2}{49}=1$