Question

ПОМОГИТЕ ПОЖАЛУЙСТА СРОЧНЛ ПРОШУ

Answer 1

$1)\; \left \{ {{2x-5y=12} \atop {4x+5y=24}} \right.\oplus \; \left \{ {{2x-5y=12} \atop {6x=36}} \right.\; \left \{ {{5y=2x-12} \atop {x=6}} \right.\; \left \{ {{5y=0} \atop {x=6}} \right. \; \left \{ {{y=0} \atop {x=6}} \right. \\\\Otvet:\; \; (6,0)\; .$

$2)\; \; \left \{ {{5x-3y=11\, |\cdot 2} \atop {2x-4y=3\, |\cdot (-5)}} \right. \left \{ {{5x-3y=11} \atop {14y=7}} \right.\; \left \{ {{5x=11+3y} \atop {y=\frac{1}{2}}} \right.\; \left \{ {{5x=12,5} \atop {y=0,5}} \right.\; \left \{ {{x=2,5} \atop {y=0,5}} \right. \\\\Otvet:\; \; (2,5\; ;\; 0,5)\; .$

$3)\; \left \{ {{7a+2b=9} \atop {3a+b=-1}} \right.\; \left \{ {{7a=9-2(-3a-1)} \atop {b=-3a-1}} \right.\; \left \{ {{7a=11+6a} \atop {b=-3a-1}} \right.\; \left \{ {{a=11} \atop {b=-34}} \right.\\\\Otvet:\; \; (11,-34)\; .$

$4)\; \; \left \{ {{3x+4y=-2} \atop {6x-7y=11}} \right.\; \left \{ {{x=\frac{-4y-2}{3}} \atop {7y=6\cdot \frac{-4y-2}{3}-11}} \right. \; \left \{ {{x=\frac{-4y-2}{3}} \atop {7y=-8y-15}} \right. \; \left \{ {{x=\frac{-4y-2}{3}} \atop {15y=-15}} \right. \\\\\left \{ {{x=\frac{2}{3}} \atop {y=-1}} \right. \\\\Otvet:\; \; (\, \frac{2}{3}\, ;-1)\; .$

Answer 2

1.
а)
$2x - 5y = 12 \\ 4x + 5y = 24 \\ \\ 6x = 36 \\ y = \frac{2x - 12}{5} \\ \\ x = 6 \\ y = \frac{2 \times 6 - 12}{5} = 0$
Ответ: (6; 0)

б)
$5x - 3y = 11 \\ 2x - 4y = 3 \\ \\ 10x - 6y = 22 \\ 10x - 20y = 15 \\ \\ 14y = 7 \\ x = \frac{3 + 4y}{2} \\ \\ y = \frac{1}{2} \\ x = \frac{3 + 4 \times \frac{1}{2} }{2} = \frac{5}{2}$
Ответ: (5/2; 1/2).

2)
а)
$7a + 2b = 9 \\ 3a + b = - 1 \\ \\ b = - 1 - 3a\\ 7a + 2( - 1 - 3a) = 9 \\ \\ b = - 1 - 3a\\ 7a - 2 - 6a = 9 \\ \\ b = - 1 - 3a \\ a = 11 \\ \\ a = 11 \\ b = - 1 - 3 \times 11 = - 34$
Ответ: (11; -34)

б)
$3x + 4y = - 2 \\ 6x - 7y = 11 \\ \\ x = \frac{ - 2 - 4y}{3} \\ 6 \times \frac{ - 2 - 4y}{3} - 7y = 11 \\ \\ x = \frac{ - 2 - 4y}{3} \\ - 4 - 8y - 7y = 11 \\ \\ - 15y = 15 \\ x = \frac{ - 2 - 4y}{3} \\ \\ y = - 1 \\ x = \frac{ - 2 - 4 \times ( - 1)}{3} = \frac{2}{3}$

Ответ: (2/3; -1)