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]
