Question

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Answer 1

$7.$

$1) \: \: \: \: \: \left \{ {{x + 2y = - 5} \atop {3x - 2y = 9}} \right.$

Т.к x+2y=-5 → x=-5-2y. Вместо х поставим выражение -5-2y

$3x - 2y = 9 \\ 3( - 5 - 2y) - 2y = 9 \\ - 15 - 6y - 2y = 9 \\ - 6y - 2y = 9 + 15 \\ - 8y = 24 \\ y = 3$

y=3. А теперь вместо у поставим 3 находим х

$x = - 5 - 2y \\ x = - 5 - 2 \times 3 \\ x = - 5 - 6 \\ x = - 11$

$2)$

$\left \{ {{4x + 3y = 8} \atop {5x - y = - 9}} \right.$

5x-y=-9 → -y=-9-5x → y=-(-9-5x)

$4x + 3y = 8 \\ 4x + ( - 3( - 9 - 5x) = 8 \\ 4x - 3( - 9 - 5x) = 8 \\ 4x + 27 + 15x = 8 \\ 4x + 15x = 8 - 27 \\ 19x = - 19 \\ x = - 1$

$y = - ( - 9 - 5x) \\ y = 9 + 5x \\ y = 9 + 5 \times 1 \\ y = 9 + 5 \\ y = 14$

$8.$

$1)$

$\left \{ {{2x + y = 5} \atop {2x - y = 3}} \right. + \\ 4x = 8 \\ x = 2 \\ \\ 2x + y = 5 \\ 2 \times 2 + y = 5 \\ 4 + y = 5 \\ y = 1$

$2)$

$\left \{ {{3x + 2y = 0} \atop {5x + 2y = 4}} \right. - \\ - 2x = - 4 \\ x = 2 \\ \\ 3x + 2y = 0 \\ 3 \times 2 + 2y = 0 \\ 6 + 2y = 0 \\ 2y = - 6 \\ y = - 3$

$3)$

$\left \{ {{4x + 3y = 3 \: \: \:| \times 2} \atop {5x - 6y = 7 \: \: \: \: \: \: \: \: \: \: \: \: }} \right. \\ \\ \left \{ {{8x + 6y = 6} \atop {5x - 6y = 7}} \right. + \\ 13x = 13 \\ x = 1 \\ \\ 4x + 3y = 3 \\ 4 \times 1 + 3y = 3 \\ 4 + 3y = 3 \\ 3y = - 1 \\ y = - \frac{1}{3}$

$4)$

$\left \{ {{5x + 7y = - 19 \: \: \:| \times 3} \atop {2x - 3y = 4 \: \: \: \: \: \: \: \: | \times 7 }} \right. \\ \\ \left \{ {{15 + 21y = - 57} \atop {14x - 21y = 28}} \right. + \\ 29x = - 29 \\ x = - 1 \\ \\ 2x - 3y = 4 \\ 2 \times ( - 1) - 3y = 4 \\ - 2 - 3y = 4 \\ - 3y = 6 \\ y = - 2$