Question

use cramer’s rule to solve the system {x-6y=2 {12x+7y=-55no solution one solution (_,_)infinitely many solutions (_,_)

Answer 1

Using Cramer's rule in solving systems.

`\begin{gathered} a_1x+b_1y=c_1 \\ a_2x+b_2y=c_2 \end{gathered}`

The solution for x and y are :

`\begin{gathered} x=\frac{b_2c_1-b_1c_2}{a_1b_2_{}-_{}a_2b_1} \\ \\ y=\frac{a_1c_2-a_2c_1}{a_1b_2_{}-a_2b_1} \end{gathered}`

From the problem, we have two equations :

`\begin{gathered} x-6y=2 \\ 12x+7y=-55 \end{gathered}`

From the equations, the values are :

`\begin{gathered} a_1=1,b_1=-6,c_1=2 \\ a_2=12,b_2=7,c_2=-55 \end{gathered}`

Using the formula above, the values of x and y are :

`\begin{gathered} x=\frac{b_2c_1-b_1c_2}{a_1b_2-_{}a_2b_1}=(7(2)-(-6)(-55))/(1(7)-12(-6)) \\ x=(14-330)/(7+72) \\ x=-4 \\ \\ y=(a_1c_2-a_2c_1)/(a_1b_2-a_2b_1)=(1(-55)-12(2))/(1(7)-12(-6)) \\ y=(-55-24)/(7+72) \\ y=-1 \end{gathered}`

The solution set is One solution. (-4, -1)