Respuesta :
By using Cramer’s Rule, the value of x is 2/7 and y is 1/2.
Cramer’s Rule;
Cramer’s Rule is defined as the determinant method to find the solution of the linear system of equations.
Given
The system of equations;
[tex]\rm 9x-2y=5\\\\-3x-4y=-4[/tex]
The Cramer's rule to find the value of x in the following system of equations.
[tex]\rm \dfrac{x}{D_1}=\dfrac{y}{D_2}=\dfrac{1}{D}[/tex]
Where;
[tex]\rm D_1=\left[\begin{array}{ccc}5&-2\\4&-4\\\end{array}\right] \\\\D_1= 5\times (-4) - 4 \times (-2)\\\\D_1=-20-(-8)\\\\D_1=-20+8\\\\D_1=-12\\\\D_2=\left[\begin{array}{ccc}9&5\\-3&-4\\\end{array}\right] \\\\D_2=9\times (-4)-5\times (-3)\\\\D_2=-36-(-15)\\\\D_1=-36+15\\\\D_1=-21\\\\D = \left[\begin{array}{ccc}9&-2\\-3&-4\\\end{array}\right] \\\\ D = 9\times(-4)-(-2)\times (-3)\\\\D=-36-6\\\\D=-42[/tex]
Therefore,
[tex]\rm \dfrac{x}{D_1}=\dfrac{y}{D_2}=\dfrac{1}{D}\\\\\rm \dfrac{x}{-12}=\dfrac{y}{-21}=\dfrac{1}{-42}\\\\ \dfrac{x}{-12}=\dfrac{1}{-42}\\\\ -42x=-12\\\\x=\dfrac{-12}{-42}\\\\x=\dfrac{2}{7}\\\\\dfrac{y}{-21}=\dfrac{1}{-42}\\\\ -42y=-21\\\\y=\dfrac{-21}{-42}\\\\y=\dfrac{1}{2}[/tex]
Hence, by using Cramer’s Rule, the value of x is 2/7 and y is 1/2.
To know more about Cramer’s Rule click the link given below.
brainly.com/question/10132289
