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If4y-(x-4)=4x+(-y+4), and neither x nor ...

If`4y-(x-4)=4x+(-y+4)`, and neither x nor y = 0, what is `(x)/(y)`?

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To solve the equation \(4y - (x - 4) = 4x + (-y + 4)\) and find the value of \(\frac{x}{y}\), we can follow these steps: ### Step 1: Simplify the equation Start with the original equation: \[ 4y - (x - 4) = 4x + (-y + 4) \] Distributing the negative sign on the left side: \[ 4y - x + 4 = 4x - y + 4 \] ### Step 2: Rearrange the equation Next, we will rearrange the equation to isolate terms involving \(x\) and \(y\). Move \(x\) and \(y\) terms to one side and constants to the other: \[ 4y + y = 4x + x + 4 - 4 \] This simplifies to: \[ 5y = 5x \] ### Step 3: Divide both sides by 5 Now, divide both sides by 5: \[ y = x \] ### Step 4: Find \(\frac{x}{y}\) Since we have \(y = x\), we can express \(\frac{x}{y}\) as: \[ \frac{x}{y} = \frac{x}{x} = 1 \] ### Final Answer Thus, the value of \(\frac{x}{y}\) is: \[ \frac{x}{y} = 1 \] ---
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