Solve the equation for y. Then find the value of y for each value of x.

Question

3 x minus 7 y equals 19​; xequalsnegative 2​, 0​, 2
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Part 1
Solve the equation for y.
yequals
  
enter your response here
​(Simplify your answer. Use integers or fractions for any numbers in the​ expression.)

Answer 1

To solve the equation \(3x - 7y = 19\) for \(y\), we can follow these steps:

1. Start with the original equation: \[ 3x - 7y = 19 \]

2. Isolate the term containing \(y\): \[ -7y = 19 - 3x \]

3. Divide by \(-7\) to solve for \(y\): \[ y = \frac{19 - 3x}{-7} \]

4. Simplify the expression: \[ y = -\frac{19}{7} + \frac{3}{7}x \]

So the equation solved for \(y\) is: \[ y = -\frac{19}{7} + \frac{3}{7}x \]

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Now, we can find the value of \(y\) for each given value of \(x\):

1. For \(x = -2\): \[ y = -\frac{19}{7} + \frac{3}{7}(-2) \] \[ y = -\frac{19}{7} - \frac{6}{7} = -\frac{25}{7} \]

2. For \(x = 0\): \[ y = -\frac{19}{7} + \frac{3}{7}(0) \] \[ y = -\frac{19}{7} \]

3. For \(x = 2\): \[ y = -\frac{19}{7} + \frac{3}{7}(2) \] \[ y = -\frac{19}{7} + \frac{6}{7} = -\frac{13}{7} \]

Summary of results:

• For \(x = -2\), \(y = -\frac{25}{7}\)
• For \(x = 0\), \(y = -\frac{19}{7}\)
• For \(x = 2\), \(y = -\frac{13}{7}\)