[latex]1)\ egin{cases}3x - 2y = 5 \ -2x + 6y = 9 end{cases}\ \ egin{cases}3x - 2y = 5/*2 \ -2x + 6y = 9/*3 end{cases}\ \ egin{cases}6x - 4y =10 \ -6x + 18y = 27 end{cases}\---------\14y=37/:14[/latex] [latex]y=frac{37}{14}=2frac{9}{14}\ \3x - 2*frac{37}{14}= 5 \ \3x = 5+frac{37}{12}\ \3x = 5+frac{37}{7}\ \3x = frac{35}{7}+frac{37}{7}[/latex] [latex]3x=frac{72}{7}/*frac{1}{3}\ \x=frac{24}{7}=3frac{3}{7}\ \egin{cases}x = 3frac{3}{7} \ y=2frac{9}{14}end{cases}[/latex] [latex]2)\ egin{cases}3 - 3x = 3y + 2 \ y + 5 = 4x - 3 end{cases}\ \ egin{cases}- 3x-3y =2-3 \ -4x+y = - 3-5 end{cases}[/latex] [latex]egin{cases}- 3x-3y =-1 \ -4x+y= -8 /*3end{cases} \ \egin{cases}- 3x-3y =-1 \ -12x+3y= -24end{cases}\---------\ -15x =-25/(-15)\ \x=frac{25}{15}=frac{5}{3}=1frac{2}{3}[/latex] [latex]y + 5 = 4*frac{5}{3}- 3\ \y=frac{20}{3}-3-5=6frac{2}{3}-8=-1frac{1}{3}\ \ egin{cases}x=1frac{2}{3} \ y =-1frac{1}{3}end{cases}[/latex] [latex]3)\ egin{cases}(x + 3)^2- (y - 1)^2= (x - y)(x + y) \ 3x - 7y = 0 end{cases}\ \ egin{cases} x^2 + 6x + 9- (y^2-2y +1) = x^2-y^2 \ 3x - 7y = 0 end{cases} \ \egin{cases} x^2 + 6x + 9- y^2+2y -1 - x^2+y^2 =0\ 3x - 7y = 0 end{cases} \ \egin{cases}6x +2y =-8/:(-2)\ 3x - 7y =-1 end{cases}[/latex] [latex]egin{cases}-3x -y =4\ 3x - 7y =0 end{cases} \--------\-8y=4/*(-8)\ \y=-frac{4}{8}=-frac{1}{2}\ \3x - 7*(-frac{1}{2}) =0\ \3x=-frac{7}{2}/*(frac{1}{3})[/latex] [latex]x=-frac{7}{6}=-1frac{1}{6}\ \egin{cases}x=-1frac{1}{6} \ y=-frac{1}{2} end{cases}[/latex]
