To use substitution to solve the system of equations given:
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Original System: \[ x + 3y = 9 \tag{1} \] \[ y = x - 5 \tag{2} \]
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Substitute \(y\) from equation (2) into equation (1):
- Start with equation (1): \(x + 3y = 9\)
- Substitute \(y = x - 5\):
\[ x + 3(x - 5) = 9 \]
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This gives us the correct first step in trying to eliminate \(y\): \[ x + 3(x - 5) = 9 \]
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Let's check the other equations presented:
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\((x - 5) + 3y = 9\) is not correct because it seems to substitute \(y\) as \(y = (x - 5)\) which doesn't apply correctly in this instance.
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\(2x + 4y = 9 - 5\) makes no sense in this context, as it does not correctly rearrange or simplify from our substitutions.
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\(x + 3x - 15 = 9\) can be derived from our valid substitution (since \(3(x - 5) = 3x - 15\)), and is an appropriate equation.
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\(4x - 15 = 9\) is correct but derived from the preceding equation \(x + 3x - 15 = 9\).
Valid Steps:
- \(x + 3(x-5) = 9\)
- From \(x + 3(x - 5) = 9\), you then could simplify to \(4x - 15 = 9\).
Thus, the correct choices for the steps in solving the system with substitution are:
- \(x + 3(x - 5) = 9\)
- \(x + 3x - 15 = 9\)
- \(4x - 15 = 9\)