Question

СРОЧНО! помогите с системой уравнений!!
1. {x+y=4
{-x+2y=2
2. {5x+2y=12
{4x+y=3​

Answer 1

Ответ:

$(2; 2);$

$(-2; 11);$

Объяснение:

$\displaystyle \left \{ {{x+y=4} \atop {-x+2y=2}} \right. \bigg | + \Leftrightarrow \left \{ {{x+y=4} \atop {-x+x+2y+y=2+4}} \right. \Leftrightarrow \left \{ {{x=4-y} \atop {3y=6}} \right. \Leftrightarrow \left \{ {{x=2} \atop {y=2}} \right. ;$

$(2; 2);$

_________________________

$\displaystyle \left \{ {{5x+2y=12} \atop {4x+y=3}} \right. \Leftrightarrow \left \{ {{5x+2(3-4x)=12} \atop {y=3-4x}} \right. \Leftrightarrow \left \{ {{5x+6-8x=12} \atop {y=3-4x}} \right. \Leftrightarrow$

$\displaystyle \Leftrightarrow \left \{ {{(5-8)x=12-6} \atop {y=3-4x}} \right. \Leftrightarrow \left \{ {{-3x=6} \atop {y=3-4x}} \right. \Leftrightarrow \left \{ {{x=-2} \atop {y=11}} \right. ;$

$(-2; 11);$