Using the equations for each line, isolate the y value on one side of each equation and then set the equations equal to one another. For example, using y = (-x) + 2, y = x + 1 and y = (-1/2)x + 1, you can say that (-x) + 2 = x + 1 = (-1/2)x + 1. As you simplify this equation, remember that the left side value is from equation #1, the middle value is from equation #2 and the right side is from equation #3.
Using this three-sided equation, perform operations to eliminate any extra numbers or x-values possible --- and be sure to perform the same operation on each of the three sections of the equation. In the example, you can add x to each side of the equation to simplify to: 2 = 2x + 1 = (1/2)x + 1. Then you can subtract 1 from each side to simplify to: 1 = 2x = (1/2)x.
Determine all possible values for x after the equation is fully simplified. This can be done by breaking the equation down into pieces and solving for x. For example, the previous equation can be broken into 1 = 2x, 1 = (1/2)x and 2x = (1/2)x, which in each situation would require that x = 1/2, x = 2 and x = 0, respectively. These are the x-value coordinates for your intersection points (x,y).
Solve the equations for the y coordinate value by plugging appropriate x values into appropriate equations; this is where it is important to remember which part of your equations originated from which one of the three separate initial equations. For example, the simplified three-part equation 1 = 2x = (1/2)x is a combination of equation #1 = equation #2 = equation #3. When breaking this simplified equation into three separate parts to find the possible values for x, you were also doing this: equation #1 = equation #2, equation #1 = equation #3 and equation #2 = equation #3. In the example, the discovered x value for equation #1 = equation #2 was x = (1/2); therefore, you must plug this value into the original equations of either equation #1 or equation #2. This value cannot be plugged into the original equation #3, because the two equations used to find this x value were #1 and #2.
Format your plot points in (x,y) format after you find each y-value. The example answers would look like this: (0,1), (2,0) and (1/2,3/2).