Question

Using Cramer’s rule, what is the value of x in the solution to the system of linear equations below?
-1/2x+3y=-4
-x-y=-1

a -2
b -1
c 1/2
d 2

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.

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

Answer 2

Using the Cramer's rule, the value of x in the system of equation is 2

How to solve for x?

The system of equation is given as:

-1/2x + 3y = -4

-x - y = -1

Represent the above equation as a matrix

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

Start by calculating the determinant of the matrix

|A| = -1/2 * -1 - 3 * -1

Evaluate

|A| = 7/2

To calculate x, we replace the first column by the last.

So, we have:

$\left[\begin{array}{cc}-4&3\\-1&-1\end{array}\right]$

Next, calculate the determinant of the matrix

|x| = -4 * -1 - 3 * -1

|x| = 7

The value of x is then calculated as:

x = |x|/|A|

This gives

x = 7 ÷ 7/2

Evaluate

x = 2

Hence, the value of x is 2

Read more about Cramer’s rule at:

https://brainly.com/question/11198799

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