Answer :
[tex]A.)\\\\-3x + 3y = 0\\x + 6y = 10 \ / *3\\\\-3x + 3y = 0\\3x + 18y = 30\\+------\\21y =30 \ / :21\\ \\y=\frac{30}{21}=\frac{10}{7}\\\\not \ true[/tex]
[tex]B.)\\\\-2x + 5y = -6 \ / \cdot 2\\4x - 2y = 4\\ \\-4x + 10y = -12 \\4x - 2y = 4 \\+-------- \\8y=-8\ /:8\\ \\y=-1\\ \\ not \ true[/tex]
[tex]C.\\\\5x - 2y = -6 \ / \cdot 2\\3x - 4y = 2 \\ \\ 10x - 4y = -12 \\ 3x- 4y = 2\\+------\\13x=-11 \ / :13\\ \\x=-\frac{11}{13}\\\\ not \ true[/tex]
[tex]D.)\\\\2x + 3y = 10\ / \cdot (-2)\\4x + 5y = 18\\\\-4x -6y =-20\\4x + 5y = 18\\+-------\\-y = -2 \ / \cdot (-1)\\ \\y=2[/tex]
[tex]2x + 3*2 = 10\\ \\2x=10-6 \\ \\2x=4 \ / :2 \\ \\ x=2 \\ \\ true[/tex]
[tex]B.)\\\\-2x + 5y = -6 \ / \cdot 2\\4x - 2y = 4\\ \\-4x + 10y = -12 \\4x - 2y = 4 \\+-------- \\8y=-8\ /:8\\ \\y=-1\\ \\ not \ true[/tex]
[tex]C.\\\\5x - 2y = -6 \ / \cdot 2\\3x - 4y = 2 \\ \\ 10x - 4y = -12 \\ 3x- 4y = 2\\+------\\13x=-11 \ / :13\\ \\x=-\frac{11}{13}\\\\ not \ true[/tex]
[tex]D.)\\\\2x + 3y = 10\ / \cdot (-2)\\4x + 5y = 18\\\\-4x -6y =-20\\4x + 5y = 18\\+-------\\-y = -2 \ / \cdot (-1)\\ \\y=2[/tex]
[tex]2x + 3*2 = 10\\ \\2x=10-6 \\ \\2x=4 \ / :2 \\ \\ x=2 \\ \\ true[/tex]
[tex]x=2\ \ \ and\ \ \ y=2\\\\A.\ \ \ \ \ \ x + 6y = 2+6\cdot2=2+12=14 \neq 10\\\\B.\ \ \ \ \ -2x + 5y =-2\cdot2+5\cdot2=-4+10=6 \neq -6\\\\C.\ \ \ \ \ \ \ 5x-2y =5\cdot2-2\cdot2=10-4=6 \neq -6\\\\D.\ \ \ \ \ \ \ 2x + 3y =2\cdot2+3\cdot2=4+3= 10\\and\ \ \ \ \ \ 4x + 5y = 4\cdot2+5\cdot2=8+10=18\\\\Ans.\ (2,\ 2)\ is\ a\ solution\ for\ system \ D[/tex]
