Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Using Cramer's Rule, what is the value of [tex]$y$[/tex] in the solution to the system of linear equations below?

[tex]\[
\begin{array}{l}
9x - 2y = 5 \\
-3x - 4y = -4
\end{array}
\][/tex]

A. [tex]\frac{\left|\begin{array}{cc}9 & 5 \\ -3 & -4\end{array}\right|}{-42} = \frac{2}{3}[/tex]

B. [tex]\frac{\left|\begin{array}{cc}9 & 5 \\ -3 & -4\end{array}\right|}{-42} = \frac{1}{2}[/tex]

C. [tex]\frac{\left|\begin{array}{cc}5 & -2 \\ -4 & -4\end{array}\right|}{-42} = \frac{2}{3}[/tex]

Sagot :

GinnyAnswer
To find the value of [tex]\( y \)[/tex] using Cramer's Rule for the given system of linear equations:

[tex]\[ \begin{array}{rcl} 9x - 2y &=& 5 \\ -3x - 4y &=& -4 \end{array} \][/tex]

we proceed with the following steps:

1. Write the coefficient matrix:

[tex]\[ \begin{pmatrix} 9 & -2 \\ -3 & -4 \end{pmatrix} \][/tex]

2. Calculate the determinant of the coefficient matrix:

[tex]\[ \text{det} = \begin{vmatrix} 9 & -2 \\ -3 & -4 \end{vmatrix} = (9 \cdot -4) - (-2 \cdot -3) = -36 - 6 = -42 \][/tex]

3. Construct the matrices required to find [tex]\( y \)[/tex] by replacing the column of [tex]\( y \)[/tex]-coefficients with the constants:

[tex]\[ \text{Matrix for finding } y = \begin{pmatrix} 9 & 5 \\ -3 & -4 \end{pmatrix} \][/tex]

4. Calculate the determinant of this new matrix:

[tex]\[ \text{det}_y = \begin{vmatrix} 9 & 5 \\ -3 & -4 \end{vmatrix} = (9 \cdot -4) - (5 \cdot -3) = -36 + 15 = -21 \][/tex]

5. Find the value of [tex]\( y \)[/tex] using Cramer's Rule which states that [tex]\( y = \frac{\text{det}_y}{\text{det}} \)[/tex]:

[tex]\[ y = \frac{-21}{-42} = \frac{1}{2} \][/tex]

So, the value of [tex]\( y \)[/tex] in the solution to the system of linear equations is [tex]\( \boxed{0.5} \)[/tex].
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.