Answer :
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]
[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]
