Question

помогите по алгебре
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Answer 1

$1)$

$\left \{ {{x - y = 2 \: \: \:| \times - 2} \atop {2x - 3y = - 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \right. \\ \\ \left \{ {{ - 2x + 4y = - 4} \atop {2x - 3y = - 1}} \right. + \\ y = - 5$

$x - y = 2 \\ x - ( - 5) = 2 \\ x + 5 = 2 \\ x = - 3$

$2)$

$\left \{ {{4x = - 6y \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \atop {7y - 2x = 20 \: \: \:| \times 2}} \right. \\ \\ \left \{ {{4x + 6y = 0} \atop {14y - 4x = 40}} \right. + \\ 20y = 40 \\ y = 2$

$4x = - 6y \\ 4x = - 6 \times 2 \\ 4x = - 12 \\ x = - 3$

$3)$

$\left \{ {{8x - 3y = 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \atop {3x + y = 9 \: \: \:| \times 3}} \right. \\ \\ \left \{ {{8x - 3y = 7} \atop {9x + 3y = 27}} \right. + \\ 17x = 34 \\ x = 2$

$3x + y = 9 \\ 3 \times 2 + y = 9 \\ 6 + y = 9 \\ y = 3$

$4)$

$\left \{ {{2(x + y) - x = - 6} \atop {3x - (x - y) = 0}} \right. \\ \\ \left \{ {{2x + 2y - x = - 6} \atop {3x - x + y = 0}} \right. \\ \\ \left \{ {{x + 2y = - 6 \: \: \:| \times ( - 2)} \atop {2x + y = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \right. \\ \\ \left \{ {{ - 2x - 4y = 12} \atop {2x + y = 0}} \right. + \\ - 3y = 12 \\ y = - 4$

$2x + y = 0 \\ 2x - 4 = 0 \\ 2x = 4 \\ x = 2$

$5)$

$\left \{ {{x + 5y = - 2 \: \: \: \: \: \: \: \: \: \: \: \: } \atop {0.5x - y = 6 \: \: \:| \times 5}} \right. \\ \\ \left \{ {{x + 5y = - 2} \atop {2.5x - 5y = 30}} \right. + \\ 3.5x = 28 \\ x = 8$

$x + 5y = - 2 \\ 8 + 5y = - 2 \\ 5y = - 10 \\ y = - 2$

$6)$

$\left \{ {{2x + 3(x + y) = 11} \atop {7(x + 3y) - 4y = - 23}} \right. \\ \\ \left \{ {{2x + 3x + 3y = 11} \atop {7x + 21y - 4y = - 23}} \right. \\ \\ \left \{ {{5x + 3y = 11 \: \: \:| \times 7} \atop {7x + 17y = - 23 \: \: \:| \times ( - 5)}} \right. \\ \\ \left \{ {{35x + 21y = 77} \atop { - 35x - 85y = - 115}} \right. + \\ - 64y = - 38 \\ y = \frac{38}{64}$

$5x + 3y = 11 \\ 5x + 3 \times \frac{38}{64} = 11 \\ 5x + \frac{114}{64} = 11 \\ 5x = 11 - \frac{114}{64} = 11 - 1 \frac{50}{64} \\ 5x = 10 \frac{64}{64} - 1 \frac{50}{64} = 9 \frac{14}{64} \\ x = \frac{590}{64} \div 5 = \frac{590}{64} \times \frac{1}{5} = \frac{118}{64} = 1 \frac{54}{64}$

Объяснение:

Система уравнение решим через методом сложение