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Question

# Solve the system of equations by using the row-reduction method.$\left\{\begin{array}{l}{3 x+4 y=1} \\ {8 x+11 y=4}\end{array}\right.$

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\begin{align*} &3x + 4y = 1 &&\\ &8x + 11y = 4 &&\\\\ & \left[\begin{array}{cc|c} 3&4&1\\ 8&11&4 \end{array}\right] && \text{Write the augmented matrix}\\\\ & \left[\begin{array}{cc|c} 1&\dfrac{4}{3}&\dfrac{1}{3}\\[2ex] 8&11&4 \end{array}\right] && \dfrac{1}{3}R_1 \rightarrow R_1\\\\ & \left[\begin{array}{cc|c} 1&\dfrac{4}{3}&\dfrac{1}{3}\\[2ex] 0&\dfrac{1}{3}&\dfrac{4}{3} \end{array}\right] && - 8R_1 + R_2 \rightarrow R_2\\\\ & \left[\begin{array}{cc|c} 1&\dfrac{4}{3}&\dfrac{1}{3}\\[2ex] 0&1&4 \end{array}\right] && 3R_2 \rightarrow R_2\\\\ & \left[\begin{array}{cc|c} 1&0&-5\\[2ex] 0&1&4 \end{array}\right] && - \dfrac{4}{3}R_2 + R_1 \rightarrow R_1 \end{align*}

$\boxed{\color{#c34632}{\text{The solution set is: \{(- 5, 4)\}}}}$

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