Question

Реши систему уравнений:

⎧⎩⎨⎪⎪(2x+y)(x+4y)=198252x+yx+4y=922

ответ:

⎧⎩⎨⎪⎪⎪⎪x1=

y1=

⎧⎩⎨⎪⎪⎪⎪x2=−

y2=−

Answer 1

( x₁ , y₁ ) = ( -$\frac{2}{5}$ , -1 )

( x₂ , y₂ ) = ( $\frac{2}{5}$, 1 )

Объяснение:

$\left \{ {{(2x+y)*(x+4y)=\frac{198}{25} } \atop {\frac{2x+y}{x+4y} =\frac{9}{22} }} \right.$

$\left \{ {{(2x+y)*(x+4y)=\frac{198}{25} } \atop {35x-14y=0}} \right.$

$\left \{ {{(2x+y)*(x+4y)=\frac{198}{25} } \atop {y=\frac{5}{2}x }} \right.$

$(2x+\frac{5}{2} x)*(x+4*\frac{5}{2} x)=\frac{198}{25}$

$x=-\frac{2}{5}$

$x=\frac{2}{5}$

$y=\frac{5}{2} *(-\frac{2}{5} )$

$y=\frac{5}{2} *\frac{2}{5}$

$y=-1$

$y=1\\$

( x₁ , y₁ ) = ( -$\frac{2}{5}$ , -1 )

( x₂ , y₂ ) = ( $\frac{2}{5}$, 1 )

Проверка

$\left \{ {{(2*(-\frac{2}{5})-1)*(-\frac{2}{5}+4*(-1))=\frac{198}{25} } \atop {\frac{2*(-\frac{2}{5} )-1}{-\frac{2}{5}+4*(-1) }=\frac{9}{22} }} \right.$

$\left \{ {{(2*\frac{2}{5} +1)*(\frac{2}{5}+1)*(\frac{2}{5}+1)*(\frac{2}{5} +4+1)=\frac{198}{25} } \atop {\frac{2*\frac{2}{5} +1}{\frac{2}{5}+4*1 }=\frac{9}{22} }} \right.$

$\left \{ {{\frac{198}{25} =\frac{198}{25} } \atop {\frac{9}{22}=\frac{9}{22} }} \right.$

$\left \{ {{\frac{198}{25} =\frac{198}{25} } \atop {\frac{9}{22}=\frac{9}{22} }} \right.$

( x₁ , y₁ ) = ( -$\frac{2}{5}$ , -1 )

( x₂ , y₂ ) = ( $\frac{2}{5}$, 1 )