Question

Срочно розв'язати систему рівнянь способом додавання

Answer 1

1)

$\displaystyle\bf\\\left \{ {{2y - x = 2 \: \: | \times ( - 2)} \atop {4y - 2x = 3 }} \right. \\ \displaystyle\bf\\ + \left \{ {{ - 4y + 2x = - 4} \atop {4y - 2x = 3 }} \right. \\ \\4y - 4y + 2x - 2x = - 4 + 3 \\ 0\neq - 1$

Ответ: нет решений

2)

$\displaystyle\bf\\\left \{ {{x - 5y = 8 \: \: | \times 4} \atop {2x + 4y = 30 \: \: | \times 5}} \right. \\ \displaystyle\bf\\ + \left \{ {{4x - 20y = 32} \atop {10x + 20y = 150 }} \right. \\ \\ 4x + 10x = 150 + 32 \\ 14x = 182 \\ x = 182 \div 14 \\ x = 13 \\ \\ 13 - 5y = 8 \\ 5y = 13 - 8 \\ 5y = 5 \\ y = 5 \div 5 \\ y = 1$

Ответ: ( 13 ; 1 )

3)

$\displaystyle\bf\\\left \{ {{6x + 5y = 2 \: \: | \times 4 } \atop {3x - 4y = 46 \: \: | \times 5 }} \right. \\ \displaystyle\bf\\ + \left \{ {{24x + 20y = 8} \atop {15x - 20y = 230 }} \right. \\ \\ 24x + 15x = 230 + 8 \\ 39x = 238 \\ x = \frac{238}{39} \\ x = 6 \frac{4}{39} \\ \\ 3 \times \frac{238}{39} - 4y = 46 \\ \frac{238}{13} - 4y = 46 \\ 4y = 18 \frac{4}{13} - 46 \\ 4y = 18 \frac{4}{13} - 45 \frac{13}{13} \\ 4y = - 27 \frac{9}{13} \\ y = - 27 \frac{9}{13} \div 4 \\ y = - \frac{360}{13 \times 4} \\ y = - \frac{90}{13} \\ y = - 6 \frac{12}{13}$

Ответ: ( 6 4/39 ; - 6 12/13 )