Solve graphically: 2x + y = 6 and 2x − y = 2. Also find the coordinates of the vertices of the triangle formed by these lines and the x-axis.

1. 1 · Write what is given and what is to be found. Lines 2x + y = 6 and 2x − y = 2. To find: the solution, and the vertices of the triangle with the x-axis.
2. 2 · Make a table for each line.
   • 2x + y = 6, so y = 6 − 2x: (0, 6), (3, 0), (2, 2)
   • 2x − y = 2, so y = 2x − 2: (0, −2), (1, 0), (2, 2)
3. 3 · Draw the graph. Draw and label both axes with a scale. Plot each set of points, join them with a ruler, extend the lines and label each line with its equation.
4. 4 · Read the meeting point. The lines meet at (2, 2). So x = 2 and y = 2.
5. 5 · Find the vertices. 2x + y = 6 cuts the x-axis at (3, 0). 2x − y = 2 cuts it at (1, 0). The triangle has vertices (2, 2), (3, 0) and (1, 0). Shade it.
6. 6 · Check and box the answer. 2(2) + 2 = 6 and 2(2) − 2 = 2. Therefore x = 2, y = 2, and the vertices are (2, 2), (1, 0) and (3, 0).

Scoring tip: Plot three points for each line, not two. If the three points are not in a straight line, you have made a mistake in the table.