a) x - y = 1 2x + 3y = 7 x=1+y 2(1+y)+3y=7 x=1+y 2+2y+3y=7 x=1+y 5y=7-2 x=1+y 5y=5/:5 x=1+y y=1 x=1+1 y=1 x=2 y=1 b) x + 2y=3 2x + y = 12 x=3-2y 2(3-2y)+y=12 x=3-2y 6-4y+y=12 x=3-2y -3y=12-6 x=3-2y -3y=6/:(-3) x=3-2y y= -2 x=3-2*(-2) y =-2 x=7 y= -2 c)2x - y = 8 x + 2y= -1 2x-y=8 x= -1-2y 2(-1-2y)-y=8 x= -1-2y -2-4y-y=8 x= -1-2y -5y=8+2 x= -1-2y -5y=10/:(-5) x= -1-2y y=-2 x= -1-2*(-2) y= -2 x=-1+4 y= -2 x=3
[latex]a)\ \egin{cases}x - y = 1 \ 2x + 3y = 7 end{cases}\ \egin{cases}y =x- 1 \ 2x + 3(x-1) = 7 end{cases}\ \egin{cases}y =x- 1 \ 2x + 3x-3 = 7 end{cases}\ \egin{cases}y =x- 1 \ 5x =10/:5 end{cases}\ \[/latex] [latex]egin{cases}y =2- 1 \ x =2 end{cases}\ \ egin{cases}y =1 \ x =2 end{cases}[/latex] [latex]b)\ \egin{cases}x + 2y=3\ 2x + y = 12 end{cases}\ \egin{cases}x + 2*(12-2x)=3\ y = 12 -2xend{cases}\ \egin{cases}x + 24-4x=3\ y = 12 -2xend{cases}\ \egin{cases}-x=-21/:(-3)\ y = 12 -2xend{cases}[/latex] [latex]egin{cases}x=7\ y = 12 -2*7end{cases}\ \egin{cases}x=7\ y = 12 -14end{cases}\ \egin{cases}x=7\ y = -2end{cases}\ \[/latex] [latex]c)\ \egin{cases}2x - y = 8\ x + 2y= -1 end{cases}\ \egin{cases}y =2x-8 \ x + 2*(2x-8)= -1 end{cases}\ \ egin{cases}y =2x-8 \ x + 4x-16= -1 end{cases}\ \ egin{cases}y =2x-8 \ 5x=15/:5 end{cases}[/latex] [latex]egin{cases}y =2*3-8 \ x=3 end{cases}\ \egin{cases}y =-2 \ x=3 end{cases}[/latex]
