Problem

Solve the following system of equations using the substitution method: \[ \begin{align*} 3x + 2y &= 12, \\ x - y &= 2. \end{align*} \]

Answer

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Answer

Step 3: Substitute \(y = \frac{6}{5}\) into \(x = y + 2\), we get \(x = \frac{6}{5} + 2 = \frac{16}{5}\).

Steps

Step 1 ：Step 1: Solve the second equation for \(x\), we get \(x = y + 2\).

Step 2 ：Step 2: Substitute \(x = y + 2\) into the first equation \(3x + 2y = 12\), we get \(3(y + 2) + 2y = 12 \rightarrow 3y + 6 + 2y = 12 \rightarrow 5y + 6 = 12 \rightarrow 5y = 6 \rightarrow y = \frac{6}{5}\).

Step 3 ：Step 3: Substitute \(y = \frac{6}{5}\) into \(x = y + 2\), we get \(x = \frac{6}{5} + 2 = \frac{16}{5}\).

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