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Using Cramer’s Rule, what is the value of x in the solution to the system of linear equations below?
2/5X + 1/4Y = 9/20
2/3X + 5/12 = 3/4

A)X = 0
B)X = 1
C)There are no solutions to the system.
D)There are infinite solutions to the system.

Sagot :

MrRoyal

Using Cramer’s Rule, the value of x is 0

How to determine the value of x?

We have:

2/5X + 1/4Y = 9/20

2/3X + 5/12 = 3/4

Represent as a matrix

[tex]\left[\begin{array}{cc}2/5&1/4\\2/3&5/12\end{array}\right] \left[\begin{array}{c}9/20&3/4\end{array}\right][/tex]

Start by calculating the determinant of the matrix

A = 2/4 * 5/12 - 2/3 * 1/4

Evaluate the product

A = 5/24 - 1/6

Evaluate the difference

A = (5 - 4)/24

|A| = 1/24

Next, replace the last column with the first

[tex]\left[\begin{array}{cc}9/20&1/4\\3/4&5/12\end{array}\right][/tex]

Calculate the determinant

|x| = 9/20 * 5/12 - 1/4 * 3/4

Evaluate the product

|x| = 3/16 - 3/16

Evaluate the difference

|x| = 0

The value of x is then calculated as:

x = |x|/|A|

So, we have:

x = 0/(1/24)

Evaluate

x = 0

Hence, the value of x is 0

Read more about Cramer's rule at:

https://brainly.com/question/11198799

#SPJ1

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