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3x-8=-4y. determin which ordered pair is a soulution to the equation

3 answers

To determine which ordered pair is a solution to the equation \(3x - 8 = -4y\), we can test specific ordered pairs \((x, y)\) by substituting the values into the equation.

Let's go through the steps:

  1. Rearrange the equation for clarity: \[ 3x + 4y = 8 \]

  2. Now, substitute different values for \(x\) and \(y\) to check if the equation holds true.

For example, assume we have the following pairs to test:

  • \( (2, 0) \)
  • \( (0, 2) \)
  • \( (4, -1) \)

Testing Ordered Pairs

  1. Testing \( (2, 0) \): \[ 3(2) + 4(0) = 6 + 0 = 6 \quad \text{(not a solution)} \]

  2. Testing \( (0, 2) \): \[ 3(0) + 4(2) = 0 + 8 = 8 \quad \text{(solution)} \]

  3. Testing \( (4, -1) \): \[ 3(4) + 4(-1) = 12 - 4 = 8 \quad \text{(solution)} \]

Summary

The ordered pairs \( (0, 2) \) and \( (4, -1) \) are solutions to the equation \(3x - 8 = -4y\). You can substitute any other pair to confirm if they are solutions or not.

now do 1.5x-2y=8

To determine which ordered pairs are solutions to the equation \(1.5x - 2y = 8\), let's consider the equation and substitute different values for \(x\) and \(y\).

Rearranging the Equation

First, we can rewrite the equation into a more familiar form: \[ 1.5x - 2y = 8 \]

Testing Ordered Pairs

Let's test some sample ordered pairs to check if they satisfy the equation. For example, we can test the following pairs:

  • \( (4, -1) \)
  • \( (0, -4) \)
  • \( (6, 3) \)

Testing Ordered Pairs

  1. Testing \( (4, -1) \): \[ 1.5(4) - 2(-1) = 6 - (-2) = 6 + 2 = 8 \quad \text{(solution)} \]

  2. Testing \( (0, -4) \): \[ 1.5(0) - 2(-4) = 0 + 8 = 8 \quad \text{(solution)} \]

  3. Testing \( (6, 3) \): \[ 1.5(6) - 2(3) = 9 - 6 = 3 \quad \text{(not a solution)} \]

Summary

The ordered pairs \( (4, -1) \) and \( (0, -4) \) are solutions to the equation \(1.5x - 2y = 8\). You may test other ordered pairs similarly to determine if they are also solutions.