4. The value of x and y can be solve by
using five solution or processes
method. This include:
1. Elimination
2. Substitution
3. Comparison
4. Graphing
5. Determinants
 Solving a system of two linear equation in
variables x and y using the Determinants.

5. ** To find a determinant you must
have a S QUA R E
M A T R I X !! **

6. Finding a 2 x 2 determinant:
a b
c d
Find the determinant :
-5 -7
11 8

7. Finding a 3 x 3 determinant :
a1 b1 c1 b2 c2 a2 c2 a2 b2
a2 b2 c2 b3 c3 a3 c3 a3 b3
a3 b3 c3
Find the determinant :
3 2 1 2 3 1 3 1 2
3 1 3 1 3 3
1 2 3
3 3 1

8. 2x+3y = 4 X=?
x + 2y = -7 Y=?
a1 = 2 ; b1 = 3 ; c1= 4
a2 = 1 ; b2 = 2 ; c2 = -7

9. S O L U TF o r
I
O c1 :b1 x
N 4 3
c2 b2 -7 2 8 – (-21) 29
= = = = 29
a1 b1 2 3 4-3 1
a2 b2 1 2
For
y
a1 c1 2 4
a2 c2 1 -7 -14 – 4 -18
= = = = -18
a1 b1 2 3 4-3 1
a2 b2 1 2

10. X = 29, Y = -18
2x + 3y = 4 X + 2y = -7
2(29) + 3(-18) = 29 + 2(-18) =
4 – 54 = 4
58 -7 + (-36) = -7
29
4=4 -7 = -7