Answer :
1.
[tex]3x-2y=9 \\ y=2x-7 \\ \\ \hbox{substitute 2x-7 for y in the 1st equation:} \\ 3x-2(2x-7)=9 \\ 3x-4x+14=9 \\ -x=9-14 \\ -x=-5 \\ x=5 \\ \\ y=2x-7=2 \times 5-7=10-7=3 \\ \\ \boxed{(x,y)=(5,3)}[/tex]
2.
[tex]y=x-4 \\ 2x+y=5 \\ \\ \hbox{substitute x-4 for y in the 2nd equation:} \\ 2x+x-4=5 \\ 3x=5+4 \\ 3x=9 \\ x=3 \\ \\ y=x-4=3-4=-1 \\ \\ \boxed{(x,y)=(3,-1)}[/tex]
3.
[tex]x+4y=6 \\ y=-x+3 \\ \\ \hbox{substitute -x+3 for y in the 1st equation:} \\ x+4(-x+3)=6 \\ x-4x+12=6 \\ -3x=6-12 \\ -3x=-6 \\ x=2 \\ \\ y=-x+3=-2+3=1 \\ \\ \boxed{(x,y)=(2,1)}[/tex]
[tex]3x-2y=9 \\ y=2x-7 \\ \\ \hbox{substitute 2x-7 for y in the 1st equation:} \\ 3x-2(2x-7)=9 \\ 3x-4x+14=9 \\ -x=9-14 \\ -x=-5 \\ x=5 \\ \\ y=2x-7=2 \times 5-7=10-7=3 \\ \\ \boxed{(x,y)=(5,3)}[/tex]
2.
[tex]y=x-4 \\ 2x+y=5 \\ \\ \hbox{substitute x-4 for y in the 2nd equation:} \\ 2x+x-4=5 \\ 3x=5+4 \\ 3x=9 \\ x=3 \\ \\ y=x-4=3-4=-1 \\ \\ \boxed{(x,y)=(3,-1)}[/tex]
3.
[tex]x+4y=6 \\ y=-x+3 \\ \\ \hbox{substitute -x+3 for y in the 1st equation:} \\ x+4(-x+3)=6 \\ x-4x+12=6 \\ -3x=6-12 \\ -3x=-6 \\ x=2 \\ \\ y=-x+3=-2+3=1 \\ \\ \boxed{(x,y)=(2,1)}[/tex]
