Question

решите пожалуйста систему:
1) x-3y=-5
2x-5y=-7

2) 3x-9y=3
2x+3y=5

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Answer 1

$\displaystyle 1)\left \{ {{x-3y=-5} \atop {2x-5y=-7}} \right. \\\\\left \{ {{x=-5+3y} \atop {2x-5y=-7}} \right.\\ \\2(-5+3y)-5y=-7\\y=3\\x=-5+3*3\\x=4\\(x,y)=(4,3)\\\\2)\left \{ {{3x-9y=3} \atop {2x+3y=5\\}} \right. \\\\\left \{ {{3x-9y=3} \atop {x=\frac{5}{2}-\frac{3}{2}y }} \right. \\\\3(\frac{5}{2}-\frac{3}{2}y)-9y=3\\ \\y=\frac{1}{3}\\ \\x=\frac{5}{2}-\frac{3}{2}*\frac{1}{3}\\ \\x=2\\ \\(x,y)=(2,\frac{1}{3})$

Answer 2

$\displaystyle\bf\\1)\\\\\left \{ {{x-3y=-5} \atop {2x-5y=-7}} \right. \\\\\\\left \{ {{x=3y-5} \atop {2\cdot(3y-5)-5y=-7}} \right. \\\\\\\left \{ {{x=3y-5} \atop {6y-10-5y=-7}} \right. \\\\\\\left \{ {{x=3y-5} \atop {y=10-7}} \right. \\\\\\\left \{ {{x=3\cdot 3-5} \atop {y=3}} \right. \\\\\\\left \{ {{x=4} \atop {y=3}} \right. \\\\\\Otvet: \ (4 \ ; \ 3)$

$\displaystyle\bf\\2)\\\\\left \{ {{3x-9y=3} \ |:3\atop {2x+3y=5}} \right. \\\\\\+\left \{ {{x-3y=1} \atop {2x+3y=5}} \right. \\---------\\3x=6\\\\x=6:3=2\\\\3y=x-1=2-1=1\\\\y=1:3=\frac{1}{3} \\\\Otvet: \ \Big(2 \ ; \ \frac{1}{3} \Big)$