1.
[tex]y=3x+3 \\
y=2x+8 \\ \\
\hbox{substitute 3x+3 for y in the 2nd equation:} \\
3x+3=2x+8 \\
3x-2x=8-3 \\
x=5 \\ \\
y=2x+8=2 \times 5+8=10+8=18 \\ \\
\boxed{(x,y)=(5,18)}[/tex]
2.
[tex]x+3y=17 \\
2x+3y=22 \\ \\
\hbox{solve the 1st equation for x:} \\
x+3y=17 \\
x=17-3y \\ \\
\hbox{substitute 17-3y for x in the 2nd equation:} \\
2(17-3y)+3y=22 \\
34-6y+3y=22 \\
-6y+3y=22-34 \\
-3y=-12 \\
y=\frac{-12}{-3} \\
y=4 \\ \\
x=17-3y=17-3 \times 4=17-12=5 \\ \\
\boxed{(x,y)=(5,4)}[/tex]
