置換法 (代入法) で連立方程式を解く

$\begin{array}{rl}4x+y& =28\\ \\ 4x+3x& =28& \text{3x を y に代入}\\ \\ 7x& =28\\ \\ x& =4\end{array}$‍

$\begin{array}{rl}y& =3x\\ \\ y& =3(4)\\ \\ y& =12\\ \end{array}$‍

$x=4$‍

$y=12$‍

$\begin{array}{rl}-3x+y& =-9\\ \\ -3(4)+3& \stackrel{?}{=}-9& \text{x = 4 と y = 3 を代入}\\ \\ -9& =-9& \text{よし!}\end{array}$‍

$\begin{array}{rl}5x+4y& =32\\ \\ 5(4)+4(3)& \stackrel{?}{=}32& \text{x = 4 と y = 3 を代入}\\ \\ 32& =32& \text{よし!}\end{array}$‍

$\begin{array}{rl}2x-3y& =-5\\ \\ 2x-3(x-1)& =-5& \text{x - 1 を y に代入}\\ \\ -x+3& =-5\\ \\ -x& =-8\\ \\ x& =8\end{array}$‍

$\begin{array}{rl}y& =x-1\\ \\ y& =8-1& \\ \\ y& =7\\ \end{array}$‍

$x=8$‍

$y=7$‍

$\begin{array}{rl}x-2y& =11\\ \\ x& =11+2y\end{array}$‍

$\begin{array}{rl}-7x-2y& =-13\\ \\ -7(11+2y)-2y& =-13& \text{11 + 2y を x に代入}\\ \\ -77-16y& =-13\\ \\ -16y& =64\\ \\ y& =-4\end{array}$‍

$\begin{array}{rl}x& =11+2y\\ \\ x& =11+2(-4)& \text{-4 を y に代入}\\ \\ x& =3\\ \end{array}$‍

$x=3$‍

$y=-4$‍

$\begin{array}{rl}-5& =5x+5y\\ \\ -1& =x+y& \text{5 で割る}\\ \\ x& =-1-y\end{array}$‍

$\begin{array}{rl}-3x-4y& =2\\ \\ -3(-1-y)-4y& =2& \text{-1-y を x に代入}\\ \\ 3-y& =2\\ \\ -y& =-1\\ \\ y& =1\end{array}$‍

$\begin{array}{rl}x& =-1-y\\ \\ x& =-1-(1)& \\ \\ x& =-2\\ \end{array}$‍

$x=-2$‍

$y=1$‍