Simultaneous Equations Graphical Solution
- David Smith
The coordinates of every point on the red line satisfy the red equation so the red line is the graph of: x + y = 6 The coordinates of every point on the blue line satisfy the blue equation so the blue line is the graph of: 5x - 2y = 2
What about (2, 4), the point of intersection of the red and blue lines? These coordinates, x = 2, y = 4 satisfy both the equations! Therefore x = 2, y = 4 represents the solution to the pair of simultaneous equations: x + y = 6 5x - 2y = 2 _______________________________________________________________________________________________ Exercise: By using the slider bars to change the equations, solve the following five pairs of simultaneous linear equations: 2x - 3y = 18 3x + 5y = 8 4x - 5y = 15 -3x + 2y = -20 2x + y = 14 3x - 2y = -7 x = 16 2x - 5y = 7 4x + 3y = 5 5x + y = -13 All the answers should be integers.