Step 1 :Rewrite the first equation as \(y = 1 - 3x\) and the second equation as \(y = -2\).
Step 2 :To graph the first equation, choose two points. When \(x = 0\), \(y = 1\). When \(x = 1\), \(y = -2\). So, we have the points (0,1) and (1,-2) for the first equation. The second equation is a horizontal line at \(y = -2\).
Step 3 :The intersection point of the two lines is the solution to the system of equations. From the graph, we can see that the two lines intersect at the point (1,-2).
Step 4 :Substitute \(x = 1\) and \(y = -2\) into the original equations to check if they are satisfied. For the first equation, \(3(1) + (-2) = 1\), which is true. For the second equation, \(-2 + 2 = 0\), which is also true.
Step 5 :So, the solution to the system of equations is \(x = 1\) and \(y = -2\).
Step 6 :\(\boxed{x = 1, y = -2}\)