Answer:
The value of x =-3 and y=1 in the system of linear equation.
Step-by-step explanation:
Given equations
-2x+3y+z=7
-4x-y-2z=15
x+2y+3z=-7
Using cramer's rule to find x and y
First we make matrix of coefficient of x,y and z and then find the determinant
[tex]A=\begin{bmatrix}-2&3&1\\-4&-1&-2\\1&2&3\end{bmatrix}[/tex]
Now we find determinant of A
|A|=-2(-3+4)-3(-12+2)+1(-8+1)
|A|=21
[tex]A_x=\begin{bmatrix}7&15&-7\\-4&-1&-2\\1&2&3\end{bmatrix}[/tex]
Determinant of Ax
|Ax|=7(-3+4)-3(45-14)+1(30-7)
|Ax|=-63
[tex]A_y=\begin{bmatrix}7&15&-7\\-4&-1&-2\\1&2&3\end{bmatrix}[/tex]
Determinant of Ay
|Ay|=-2(45-14)-7(-12+2)+1(28-15)
|Ay|=21
[tex]A_z=\begin{bmatrix}-2&3&1\\-4&-1&-2\\7&15&-7\end{bmatrix}[/tex]
Determinant of Az
|Az|=-2(7-30)-3(28-15)+7(-8+1)
|Az|=-42
Now we find for x, y and z
[tex]x=\dfrac{|A_x|}{|A|}\Rightarrow \dfrac{-63}{21}=-3[/tex]
[tex]y=\dfrac{|A_y|}{|A|}\Rightarrow \dfrac{21}{21}=1[/tex]
[tex]z=\dfrac{|A_z|}{|A|}\Rightarrow \dfrac{-42}{21}=-2[/tex]
Thus, The value of x =-3 and y=1 in the system of linear equation.
