Graphical Solution of Simultaneous Equations

Simultaneous equations can also be solved graphically. Knowledge of plotting linear and quadratic graphs is needed to solve equations graphically.

The solution point from the graph is the point where the two graphs intersect (cross one another.)

Example 3.1.1:

Use graphical method to solve the following pairs of simultaneous equations

(i) y = 3x – 5      and     y = -2x -7
(ii) 4y – 2x = 4     and    2y + x = 10

Solution (i):

When plotting the graph of a linear curve, it is sufficient to get 2 or 3 points.

The coordinates of points of intersection of the curves give the solution to the equations.

y = -2x – 7

y = 3x – 5

Diagram of Simultaneous Equation Graph

Intersection x = -0.4,  y = -6.2      

Solution ⇒    (-0.4, -6.2)

ii.

4y – 2x = 4

y = \( \frac{x}{2} \: + \: \scriptsize 1 \)

2y + x = 10

y = \( \frac{-x}{2} \: + \: \scriptsize 5 \)

Diagram of Simultaneous Equation Graph 

At the intersection the coordinates is given as x = 4,  y = 3

Solution ⇒      (4,  3).