Question

Помогите пожалуйста

Answer 1

Решение:

$\left \{ {{4x-5y=2} \atop {2x+10y=20}} \right. \Rightarrow \left \{ {{4x=2+5y |:4} \atop {2x+10y=20}} \right. \Rightarrow \left \{ {{x=\frac{1}{2}+\frac{5}{4}y} \atop {2x+10y=20}} \right. \\2(\frac{1}{2}+\frac{5}{4}y)+10y=20\\1+\frac{5}{2}y+10y=20\\1+\frac{5}{2}y+\frac{20}{2}y=20\\1+\frac{25}{2}y=20|*2\\2+25y=40\\25y=40-2\\25y=38\\y=\frac{38}{25} \\y = 1,52\\x=\frac{1}{2}+\frac{5}{4}*\frac{38}{25}=\frac{1}{2}+\frac{1}{2}*\frac{19}{5}=\frac{1}{2}+\frac{19}{10}=\frac{24}{10}=\frac{12}{5}=2,4$

Проверка:

$\left \{ {{4*\frac{12}{5}-5*\frac{38}{25}=2} \atop {2*\frac{12}{5}+10*\frac{38}{25}=20}} \right. \Rightarrow \left \{ {{\frac{48}{5}-\frac{38}{5}=2} \atop {\frac{24}{5}+\frac{380}{25}=20}} \right. \Rightarrow \left \{ {{\frac{10}{5}=2} \atop {\frac{120}{25}+\frac{380}{25}=20}} \right. \Rightarrow \left \{{{2=2} \atop {\frac{500}{25}=20}} \right. \Rightarrow \left \{ {{2=2} \atop {20=20}} \right.$ - Все верно

Ответ: $(x;y)=(\frac{12}{5};\frac{38}{25})$ или $(x;y) = (2,4;1,52)$