Write a system of linear equations for the graph below.

We need to determine the equation of both lines first.
Now that we know the equations, we can set up a system of equations for this graph where both equations are in standard form.
Line 1:
[tex]y = -2x + 3\\\\2x + y = 3[/tex]
Line 2:
[tex]y = -\frac{1}{3}x - 2\\\\\frac{1}{3}x + y = -2[/tex]
Final answer:
[tex]2x + y = 3\\\frac{1}{3}x + y = -2[/tex]