Solve the second equation for \(x\): \(x = y + 3\).
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- Cancel the common factor: \(\lim_{x \to 3} (x + 3)\).
- Substitute \(x = 3\): \(3 + 3 = 6\).
- Solve the system of equations: \(2x + 3y = 12\) and \(x - y = 3\).
- Substitute into the first equation: \(2(y + 3) + 3y = 12\).
- Simplify: \(2y + 6 + 3y = 12\), \(5y + 6 = 12\), \(5y = 6\).
- Divide by 5: \(y = \frac{6}{5}\).
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Let \( d \) be the distance between City A and City B.
Time from A to B = \( \frac{d}{80} \)
Time from B to A = \( \frac{d}{100} \)
Total time = \( \frac{d}{80} + \frac{d}{100} = 9 \)
Finding a common denominator:
\( \frac{5d + 4d}{400} = 9 \)
\( \frac{9d}{400} = 9 \)
\( 9d = 3600 \)
\( d = 400 \)
#### 400 kilometers