Use Cramers Rule to solve the system
2x - 3y = 11
-6x + 8y = 34
2 answers:
Step-by-step explanation:
given :
2x - 3y = 11
-6x + 8y = 34
find : the solutions of the system by using Cramers Rule.
solutions:
in the matrix 2x2 form =>
[ 2 -3] [x] [11]
=
[-6 8] [ y] [34]
D =
| 2 -3 |
|-6 8 |
= 8×2 - (-3) (-6)
= 16-18 = -2
Dx = | 11 -3 |
| 34 8 |
= 11×8 - (-3) (34)
= 88 + 102
= 190
Dy = | 2 11 |
|-6 34 |
= 2×34 - (-6) (11)
= 68 + 66
= 134
x = Dx/D = 190/-2 = -95
y = Dy/D = 134/-2 = -67
the solutions = {-95, -67}
Answer:
(x , y ) = ( -95, -67)
Step-by-step explanation:
Given system :-
2x - 3y = 11
-6x + 8y = 34
Find :- Solutions of system by using Cramers rule.
Solution :-
To solve the system using Cramer's rule, list all needed determinants.



- Evaluate the determinants.
D = 8 × 2 - ( -3) ( -6 )
= 16 - 18 = -2
= 11 × 8 - ( -3 ) ( 34 )
= 88 + 102 = 190
= 2 × 34 - ( 11 ) ( -6 )
= 68 + 66 = 134
- Since D ≠ 0, Cramer'rs rule can be applied , so find x , y using the formulas;- x =
, y =
.
Plug the value into the formula:-
x =
, y =
.
Divide
x = -95 , y = -67
- The possible solution of the system is the ordered pair ( x , y ).
(x , y ) = ( -95, -67)
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