Question

Use Cramers Rule to solve the system
2x - 3y = 11
-6x + 8y = 34

Answer 1

(x , y ) = ( -95, -67)

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.

`D = \left|\begin{array}{cc}2& - 3 \\ - 6 & 8\end{array}\right|`

`D_1 = \left|\begin{array}{cc}11 & - 3 \\ 34 & 8\end{array}\right|`

`D_2 = \left|\begin{array}{cc} 2& 11 \\ - 6 & 34\end{array}\right|`

• Evaluate the determinants.

D = 8 × 2 - ( -3) ( -6 )

= 16 - 18 = -2

`D_1` = 11 × 8 - ( -3 ) ( 34 )

= 88 + 102 = 190

`D_2` = 2 × 34 - ( 11 ) ( -6 )

= 68 + 66 = 134

• Since D ≠ 0, Cramer'rs rule can be applied , so find x , y using the formulas;- x =
  `(D_1)/(D)` , y =
  `(D_2)/(D)`.

Plug the value into the formula:-

x =
`(190)/(-2)\\` , y =
`(134)/(-2) \\`.

Divide

x = -95 , y = -67

• The possible solution of the system is the ordered pair ( x , y ).

(x , y ) = ( -95, -67)

Answer 2

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}