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Answer :

Explanation

We need to solve the following system of equations:

[tex]\begin{gathered} y=-8x \\ 2x+4y=0 \end{gathered}[/tex]

We can use the substitution method. The first equation gives us an expression of y dependent on x. We can take the second equation and replace y by that expression so we obtain an equation with only one variable:

[tex]\begin{gathered} 2x+4y=0 \\ 2x+4\cdot(-8x)=0 \\ 2x-32x=0 \\ (2-32)x=0 \\ -30x=0 \end{gathered}[/tex]

Then we divide both sides by -30:

[tex]\begin{gathered} \frac{-30x}{-30}=\frac{0}{-30} \\ x=0 \end{gathered}[/tex]

So we have found that x=0. We use this value in the expression of y:

[tex]y=-8x=-8\cdot0=0[/tex]

So we have x=0 and y=0.

Answer

Then the answer is (0,0).

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