Line 1:
[tex]x_1=-2 \\ y_1=-4 \\ \\ x_2=-1 \\ y_2=-1 \\ \\
m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-(-4)}{-1-(-2)}=\frac{-1+4}{-1+2}=\frac{3}{1}=3 \\ \\
y=3x+b \\
(-1,-1) \\
-1=3 \times (-1)+b \\
-1=-3+b \\
-1+3=b \\
b=2 \\ \\
y=3x+2[/tex]
Line 2:
[tex]x_1=2 \\ y_1=3 \\ \\ x_2=3 \\ y_2=1 \\ \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-3}{3-2}=\frac{-2}{1}=-2 \\ \\
y=-2x+b \\
(3,1) \\
1=-2 \times 3+b \\
1=-6+b \\
1+6=b \\
b=7 \\ \\
y=-2x+7[/tex]
The system of equations is:
[tex]y=3x+2 \\
y=-2x+7 \\ \\
y=y \\
3x+2=-2x+7 \\
3x+2x=7-2 \\
5x=5 \\
x=\frac{5}{5} \\
x=1 \\ \\
y=3x+2=3 \times 1+2=3+2=5 \\ \\
\boxed{(x,y)=(1,5)}[/tex]
