Question

Using Cramer’s rule, what is the value of x in the solution to the system of linear equations below?

Answer 1

9514 1404 393

Answer:

  d  2

Step-by-step explanation:

The system of equations can be written in augmented matrix form as ...

  $\displaystyle\left[\begin{array}{cc|c}-\frac{1}{2}&3&-4\\-1&-1&-1\end{array}\right]$

The value of x found by Cramer's rule is the ratio of two determinants. The numerator is the coefficient matrix with the x-column replaced by the constant column. The denominator is the coefficient matrix.

  $\displaystyle x=\frac{\left|\begin{array}{cc}-4&3\\-1&-1\end{array}\right| }{\left|\begin{array}{cc}-\frac{1}{2}&3\\-1&-1\end{array}\right|}=\frac{(-4)(-1)-(-1)(3)}{(-\frac{1}{2})(-1)-(-1)(3)}=\frac{4+3}{\frac{1}{2}+3}\\\\\boxed{x=2}$