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-2x=7y-13 ; x=3

Answer to this problem above is y=-2/7x+13/7 : y=1

This is not in slope intercept form please don’t solve it for that. Just make sure it matches the answer above pelease thank you

1 answer

To verify that the equation \(-2x = 7y - 13\) leads to \(y = -\frac{2}{7}x + \frac{13}{7}\) and also to confirm if it equals \(y = 1\) for \(x = 3\), we’ll substitute \(x = 3\) into the equation.

  1. Let's start with your equation: \[ -2x = 7y - 13 \]

  2. Substitute \(x = 3\): \[ -2(3) = 7y - 13 \] \[ -6 = 7y - 13 \]

  3. Add 13 to both sides: \[ -6 + 13 = 7y \] \[ 7 = 7y \]

  4. Dividing both sides by 7 gives: \[ y = 1 \]

Now let’s also verify that \(-2x = 7y - 13\) can be rewritten in the slope-intercept form you mentioned.

  1. Start with the original equation: \[ -2x = 7y - 13 \]

  2. Rearranging to solve for \(y\): \[ 7y = -2x + 13 \] \[ y = -\frac{2}{7}x + \frac{13}{7} \]

This confirms that your initial rewriting is correct.

So we have:

  • From the equation, when \(x = 3\), \(y = 1\).
  • The slope-intercept form of the equation is indeed \(y = -\frac{2}{7}x + \frac{13}{7}\).

Thus, both conditions you stated are satisfied.