Question

What is the solution to the system?

Line 1
x y
–2 –4
–1 –1
Line 2
x y
2 3
3 1

( , )

Answer 1

Line 1:

`x_1=-2 \\ y_1=-4 \\ \\ x_2=-1 \\ y_2=-1 \\ \\ m=(y_2-y_1)/(x_2-x_1)=(-1-(-4))/(-1-(-2))=(-1+4)/(-1+2)=(3)/(1)=3 \\ \\ y=3x+b \\ (-1,-1) \\ -1=3 * (-1)+b \\ -1=-3+b \\ -1+3=b \\ b=2 \\ \\ y=3x+2`

Line 2:

`x_1=2 \\ y_1=3 \\ \\ x_2=3 \\ y_2=1 \\ \\ m=(y_2-y_1)/(x_2-x_1)=(1-3)/(3-2)=(-2)/(1)=-2 \\ \\ y=-2x+b \\ (3,1) \\ 1=-2 * 3+b \\ 1=-6+b \\ 1+6=b \\ b=7 \\ \\ y=-2x+7`

The system of equations is:

`y=3x+2 \\ y=-2x+7 \\ \\ y=y \\ 3x+2=-2x+7 \\ 3x+2x=7-2 \\ 5x=5 \\ x=(5)/(5) \\ x=1 \\ \\ y=3x+2=3 * 1+2=3+2=5 \\ \\ \boxed{(x,y)=(1,5)}`