Worked example Solve the following simultaneous equations graphically.
x + y − 3 = 0 Solution and 4x + 2y − 8 = 0
y = 3
y = 4
x = 3
y -intercept = 3 x -intercept = 3
x = 2
y -intercept = 4 x -intercept = 2
✓ y Parallel lines do not intersect (cross), so they have no point of intersection.
There is no solution for those simultaneous equations represented by parallel lines. That means there is no set of values that will satisfy both equations simultaneously.
Discuss and discover
Working with a classmate, investigate whether the lines represented by the following equations are parallel or not. Justify your answer.