Задача 46669 «Системы линейных уравнений методом...

dlld777

2020-04-10 19:49:52

«Системы линейных уравнений методом подстановки»
вариант 2

sova

2020-04-10 20:21:00

★

1
a)

[m]\left\{\begin{matrix} y=2x & \\ 4x+5y=28 & \end{matrix}\right.\left\{\begin{matrix} y=2x & \\ 4x+5\cdot 2x=28 & \end{matrix}\right.\left\{\begin{matrix} y=2x & \\ 14x=28 & \end{matrix}\right.\left\{\begin{matrix} y=2\cdot 2 & \\ x=2 & \end{matrix}\right.[/m]

б)

[m]\left\{\begin{matrix} 2u-v=3 & \\ 7u+3v=4 & \end{matrix}\right.\left\{\begin{matrix} 2u-3=v & \\ 7u+3\cdot(2u-3)=4 & \end{matrix}\right.\left\{\begin{matrix} v=2u-3 & \\7u+6u-9=4 & \end{matrix}\right.[/m]

[m]\left\{\begin{matrix}v=2u-3 \cdot 2 & \\ 13u=13 & \end{matrix}\right..\left\{\begin{matrix}v=2\cdot -3 \cdot 2 & \\ u=1 & \end{matrix}\right..\left\{\begin{matrix}v=-1 \cdot 2 & \\ u=1 & \end{matrix}\right.[/m]

в)

[m]\left\{\begin{matrix} p-3q=1 & \\ p^2-9q=7 & \end{matrix}\right.\left\{\begin{matrix} p=3q+1 & \\(3q+1)^2-9q=7 & \end{matrix}\right.\left\{\begin{matrix} p=3q+1 & \\9q^2+6q+1-9q=7 & \end{matrix}\right.[/m]


[m]\left\{\begin{matrix} p=3q+1 & \\9q^2-3q+1=0 & \end{matrix}\right.
\left\{\begin{matrix} p=3q+1 & \\(3q-1)^2=0 & \end{matrix}\right.\left\{\begin{matrix} p=3q+1 & \\3q-1=0 & \end{matrix}\right.[/m]

[m]\left\{\begin{matrix} p=3\cdot \frac{1}{3} +1 & \\q=\frac{1}{3} & \end{matrix}\right.\left\{\begin{matrix} p=2 & \\q=\frac{1}{3} & \end{matrix}\right.[/m]


г)


[m]\left\{\begin{matrix} x=2z\\y-z+3=0 \\ x+y+z=0 \end{matrix}\right.\left\{\begin{matrix} x=2z\\y=z-3 \\ 2z+(z-3)+z=0 \end{matrix}\right.\left\{\begin{matrix} x=2z\\y=z-3 \\ 4z=3 \end{matrix}\right.\left\{\begin{matrix} x=2\cdot\frac{3}{4} \\y=\frac{3}{4}-3 \\ z=\frac{3}{4} \end{matrix}\right.[/m]

[m]\left\{\begin{matrix} x=\frac{3}{2} \\y=-\frac{9}{4} \\ z=\frac{3}{4} \end{matrix}\right.[/m]