Question

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

Answer 1

We will have the following system:

$\begin{cases}y=-\frac{3}{2}x-29 \\ y=\frac{3}{2}x+7\end{cases}$

***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:

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

Slope line 2:

$m_2=\frac{-14-(-11)}{-10-(-12)}\Rightarrow m_2=-\frac{3}{2}$

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

Line 1:

$y+8=\frac{3}{2}(x+10)\Rightarrow y+8=\frac{3}{2}x+15$$\Rightarrow y=\frac{3}{2}x+7$

Line 2:

$y+14=-\frac{3}{2}(x+10)\Rightarrow y+14=-\frac{3}{2}x-15$$\Rightarrow y=-\frac{3}{2}x-29$