Question

5.23. Rozwiąż dany układ równań metodą podstawiania. ​

Answer 1

[tex]d)\\\\\begin{cases}3x-8-(5x+4y)=x-2y\\4-2(x-y)+3x=0\end{cases}\\\\\\\begin{cases}3x-8-5x-4y=x-2y\\4-2x+2y+3x=0\end{cases}\\\\\\\begin{cases}-2x-4y-x+2y=8\\x+2y=-4\end{cases}\\\\\\\begin{cases}-3x-2y=8\\x+2y=-4\end{cases}\\\\\\\begin{cases}-3x-2y=8\\x=-4-2y\end{cases}\\\\\\-3(-4-2y)-2y=8\\\\12+6y-2y=8\\\\4y=8-12\\\\4y=-4\ \ |:4\\\\y=-1\\\\\\x=-4-2\cdot(-1)=-4+2=-2\\\\\\\begin{cases}x=-2\\y=-1\end{cases}[/tex]

[tex]f)\\\\\begin{cases}x+3y-2(x-y)=4(y+6)\\3(4x-y)-11(x+y)=5-13y\end{cases}\\\\\\\begin{cases}x+3y-2x+2y=4y+24\\12x-3y-11x-11y=5-13y\end{cases}\\\\\\\begin{cases}-x+5y-4y=24\\x-14y+13y=5\end{cases}\\\\\\\begin{cases}-x+y=24\\x-y=5\end{cases}\\\\\\\begin{cases}y=24+x\\x-y=5\end{cases}\\\\\\x-(24+x)=5\\\\x-24-x=5\\\\x-x=5+24\\\\0=29\\\\L\neq P[/tex]

Układ równań sprzeczny nie ma rozwiązania