Unit 5 - Objective 5 - Solving 2 Equations in 2 Unknowns by Determinants

Another method to solve 2 equations in 2 unknowns is by using determinants:
If a, b, c, and d are any four real numbers, then the symbol

u5obj5-01.gif (318 bytes)

is called a 2 x 2 determinant.  The numbers a, b, c, and d are called the elements of the determinant.  The value of a determinant is called the number ad - cb  so

u5obj5-02.gif (527 bytes)

We can use Cramer's rule to solve two linear equations in 2 unknowns.  If we have

a1x + b1y = c1
a2x + b2y = c2
then

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Examples: Solve the following using Cramer s Rule

1. 2x - 3y = 2
3x + 2y = 3

u5obj5-04.gif (6669 bytes)

The above answer for x should be [(2)(2)-(3)(-3)]/[(2)(2)-(3)(-3)] which equals (4+9)/(4+9) which equals 1

The above answer for y should be [(2)(3)-(3)(2)]/13 which equals 0/13 which is 0

So (1, 0) satisfied the two equations

 

2. x + 3y = 7
2x + 3y = 5

u5obj5-05.gif (3779 bytes)

So (-2, 3) is the solution that satisfies both equations.

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