In order to graph a line we just need to specify two points of it and then join them, we do this by replacing an x-value and calculating its corresponding y-value.
• y = x + 2
By replacing 0 for x we get:
y = 0 + 2
y = 2
Then, the line passes through the point (0, 2)
By replacing 1 for x:
y = 1 + 2
y = 3
Then, the line passes through the point (1, 3)
• 2x + y = 8
By isolating y on one side, we get:
y = 8 - 2x
By replacing 0 for x we get:
y = 8 - 2×0
y = 8
Then, the line passes through the point (0, 8)
By replacing 1 for x, we get:
y = 8 - 2×1
y = 8 - 2
y = 6
This line passes through the point (1, 6)
Now that we know 2 points of each line we can plot them like this:
As you can see in the graph, the lines intersect at (2, 4), then (2, 4) is the solution for the system of equations.