連立方程式
(1)
\( \left\{ \begin{array}{l} 2x+3y=1&・・・① \\ 3x-3y=4&・・・② \end{array} \right. \)
\( \begin{array}{l} &2x+3y&=1 &① \\ +)&3x-3y&=4 &② \\ \hline &5x&= 5 \\ &x&=1 \end{array} \)
①に代入して
\( \begin{align} 2 \times 1 +3y &=1 \\ y&=-\frac{1}{3} \end{align} \)
\(x=1,y=-\frac{1}{3}\)
(2)
\( \left\{ \begin{array}{l} 3x+2y=5&・・・① \\ 2x+y=2&・・・② \end{array} \right. \)
\( \begin{array}{l} &3x+2y&=5 &① \\ -)&4x+2y&=4 &②\times2 \\ \hline &-x&=1 \\ &x&=-1 \end{array} \)
②に代入して
\( \begin{align} 2 \times (-1) +y &=2 \\ y&=4 \end{align} \)
\(x=-1,y=4\)
(3)
\( \left\{ \begin{array}{l} 2x+3y=2&・・・① \\ 3x+5y=4&・・・② \end{array} \right. \)
\( \begin{align} 6x+9y&=6 &①\times3 \\ -)6x+10y&=8 &②\times2 \\ \hline -y&=-2 \\ y&=2 \end{align} \)
①に代入して
\( \begin{align} 2x+3\times2 &=2 \\ x&=-2 \end{align} \)
\(x=-2,y=2\)
(4)
\( \left\{ \begin{array}{l} 2x+3y=6&・・・① \\ x=2y-4&・・・② \end{array} \right. \)
②を①に代入して
\( \begin{align} 2(2y-4)+3y&=6 \\ 4y-8+3y&=6 \\ 7y&=14 \\ y&=2 \end{align} \)
②に代入して
\( \begin{array}{l} x=2\times2-4 \\ x=0 \end{array} \)
\(x=0,y=2\)