Question

Write a system of equations with the solution (-12,-11) in standard form

Answer 1

We will have the following system:

`\begin{cases}y=-(3)/(2)x-29 \\ y=(3)/(2)x+7\end{cases}`

***We can determine a system with the solution (-12, -11) by setting this and two other points, then creating two lines that pass by this point and the new two points.

*I chose the points (-10, -8) & (-10, -14).

So, we find the slope for each new line:

Slope line 1:

`m_1=(-8-(-11))/(-10-(-12))\Rightarrow m_1=(3)/(2)_{}`

Slope line 2:

`m_2=(-14-(-11))/(-10-(-12))\Rightarrow m_2=-(3)/(2)`

Now, using the slopes and the points we will write the equations of the lines:

Line 1:

`y+8=(3)/(2)(x+10)\Rightarrow y+8=(3)/(2)x+15`
`\Rightarrow y=(3)/(2)x+7`

Line 2:

`y+14=-(3)/(2)(x+10)\Rightarrow y+14=-(3)/(2)x-15`
`\Rightarrow y=-(3)/(2)x-29`