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Find an ordered pair \( (x, y) \) that is a solution to the equation. \( 3 x-y=9 \) \( (x, y)=(\square), \square) \)

Ask by Warner Lynch. in the United States
Feb 02,2025

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One solution is \( (4, 3) \).

Solución

Solve the equation \( 3x-y=9 \). Solve the equation by following steps: - step0: Solve for \(x\): \(3x-y=9\) - step1: Move the expression to the right side: \(3x=9+y\) - step2: Divide both sides: \(\frac{3x}{3}=\frac{9+y}{3}\) - step3: Divide the numbers: \(x=\frac{9+y}{3}\) The solution to the equation \(3x-y=9\) is \(x=\frac{9+y}{3}\). To find an ordered pair \((x, y)\) that is a solution to the equation, we need to find values of \(x\) and \(y\) that satisfy the equation. Let's choose a value for \(y\) and substitute it into the equation to find the corresponding value of \(x\). For example, if we choose \(y=3\), we can substitute it into the equation to find the value of \(x\): \[3x-3=9\] Solving for \(x\), we get: \[3x=12\] \[x=4\] Therefore, one ordered pair that is a solution to the equation is \((x, y) = (4, 3)\).

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The Deep Dive

To find an ordered pair \( (x, y) \) that satisfies the equation \( 3x - y = 9 \), we can choose a value for \( x \) and then solve for \( y \). Let's take \( x = 4 \) as an example. Substituting \( 4 \) into the equation: \[ 3(4) - y = 9 \] \[ 12 - y = 9 \] Now, solve for \( y \): \[ -y = 9 - 12 \\ -y = -3 \\ y = 3 \] So one solution is \( (x, y) = (4, 3) \). Thus, the ordered pair is \( (x, y) = (4, 3) \).

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