4.8 Solving Simultaneous Linear Equations using Matrices
1. Two simultaneous linear equations can be written in the matrix equation form.
For example, in the simultaneous equations:
ax + by = c
dx + ey = f
can be written in the matrix form as follows:
Where a, b, c, d, e and f are constant while x and y are unknowns.
Write the following simultaneous linear equations in the matrix form.
y – 6x – 19 = 0
2y + 3x + 22 = 0
– 6x + y = 19
3x + 2y = – 22
The matrix form is:
2. Matrix equations in the form
can be solved for the unknowns x and y as follows.
(a) Let and find A-1.
(b) Multiply both sides of the equation by A-1.
Solve the following simultaneous equations by using the matrix method.
2x = 5 – 3y
7x = 1 – 5y
2x + 3y = 5
7x + 5y = 1