Question

3.Решите системы уравнений: а) способом подстановки б) способом сложения x-3y = 1, (4x + 2y = -38 (7x-5y = -63 2x + y = -1​

Answer 1

а)

$\displaystyle\bf\\\left \{ {{x - 3y = 1} \atop {4x + 2y = - 38 }} \right. \\ \displaystyle\bf\\\left \{ {{x = 3y + 1} \atop {4(3y + 1) + 2y = - 38 }} \right. \\ \\ 12y + 4 + 2y = - 38 \\ 14y = - 38 - 4 \\ 14y = - 42 \\ y = - 42 \div 14 \\ y = - 3 \\ \\ x = 3 \times ( - 3) + 1 \\ x = - 9 + 1 \\ x= - 8$

Ответ: ( - 8 ; - 3 )

б)

$\displaystyle\bf\\\left \{ {{7x - 5 y= - 63} \atop {2x + y = - 1 \: \: | \times 5 }} \right. \\ \displaystyle\bf\\ + \left \{ {{7x - 5y = - 63} \atop {10x + 5y = - 5 }} \right. \\ \\ 7x + 10x = - 63 - 5 \\ 17x = - 68 \\ x = - 68 \div 17 \\ x = - 4 \\ \\ 2 \times ( - 4) + y = - 1 \\ - 8 + y = - 1 \\ y = - 1 + 8 \\ y = 7$

Ответ: ( - 4 ; 7 )