# Simultaneous Equations Graphical Solution

- Author:
- David Smith

- Topic:
- Equations, Intersection, Straight Lines

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
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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.