Question

Which system of equation is graphed? Mark only one oval Y-1/3x=0;x-y=-2X-y=2;y-3x=0Y-3x0;x-y=-2Y-1/3x=0;x-y=2

Answer 1

The formula to calculate the equation of a line between two points is

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Let us pick any two points for both the two lines and find the equation of the lines.

Line 1

`\begin{gathered} (x_1,y_1)=(-2,0) \\ (x_2,y_2)=(1,3) \end{gathered}`

Therefore,

`\begin{gathered} (y-0)/(x--2)=(3-0)/(1--2) \\ (y)/(x+2)=(3)/(1+2) \\ (y)/(x+2)=(3)/(3) \\ (y)/(x+2)=1 \\ y=1(x+2) \\ y=x+2 \\ x-y=-2...........1 \end{gathered}`

Hence, the equation of the line is

`x-y=-2..........1`

Line 2

`\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,3) \end{gathered}`

Therefore,

`\begin{gathered} (y-0)/(x-0)=(3-0)/(1-0) \\ (y)/(x)=(3)/(1) \\ (y)/(x)=3 \\ y=3x \\ y-3x=0.............2 \end{gathered}`

Hence, the equation of the line is,

`y-3x=0...............2`

Therefore, the system of equations are

`y-3x=0;x-y=-2\text{ \lparen Option 3\rparen}`