Problem

\( \left\{\begin{array}{l}3 x-2 y=4 \\ 2 x+3 y=7\end{array}\right. \)

Answer

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Answer

\begin{aligned} 3x-2y &= 4 \\[0.5em] 3\left(\dfrac{11}{5}\right) - 2y &= 4 \\[0.5em] 2y &= 3\left(\dfrac{11}{5}\right) - 4 \\[0.5em] y &= -1 \end{aligned}

Steps

Step 1 ：Add the two equations together to eliminate y:

Step 2 ：\begin{aligned} 3x-2y+2x+3y &= 4+7 \\[0.5em] 5x &= 11 \\[0.5em] x &= \dfrac{11}{5} \end{aligned}

Step 3 ：Substitute x back into one of the original equations to solve for y:

Step 4 ：\begin{aligned} 3x-2y &= 4 \\[0.5em] 3\left(\dfrac{11}{5}\right) - 2y &= 4 \\[0.5em] 2y &= 3\left(\dfrac{11}{5}\right) - 4 \\[0.5em] y &= -1 \end{aligned}

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