The x-value of the solution for the system of equations
[tex]\frac{\begin{vmatrix}148 \;\; 14\\ 246\;\;\; 5\end{vmatrix}}{\begin{vmatrix}-2 \;\; 14\\ 3\;\;\; 5\end{vmatrix}} =52[/tex]
System of linear equations
Linear equation with two variables is of the form [tex]ax+by=c[/tex]
system of linear equations is a set of two linear equations with two variables.
Given system of equations
[tex]-2x+14y=148\\3x+5y=246[/tex]
Cramer's rule
For system of linear equations of the form
[tex]ax+by=e\\cx+dy=f[/tex]
the x value is
[tex]\frac{\begin{vmatrix}e\;\; b\\ f\;\;\; d\end{vmatrix}}{\begin{vmatrix}a \;\; b\\ c\;\;\; d\end{vmatrix}}[/tex]
We apply Cramer's rule to find out the x value .
To find the x value of the system of equation , we take the determinant of x matrix divide by the determinant of coefficient matrix.
Coefficient matrix contains coefficients of x and y
[tex]\begin{vmatrix}-2 \;\; 14\\ 3\;\;\; 5\end{vmatrix}[/tex]
For determinant of x -value of matrix , we replace coefficient of x by the constants.
[tex]\begin{vmatrix}148 \;\; 14\\ 246\;\;\; 5\end{vmatrix}[/tex]
To find out x values we divide determinant of x value by the coefficient matrix
[tex]\frac{\begin{vmatrix}148 \;\; 14\\ 246\;\;\; 5\end{vmatrix}}{\begin{vmatrix}-2 \;\; 14\\ 3\;\;\; 5\end{vmatrix}}[/tex]
Now find out the value of determinant to simplify it
[tex]\frac{\begin{vmatrix}148 \;\; 14\\ 246\;\;\; 5\end{vmatrix}}{\begin{vmatrix}-2 \;\; 14\\ 3\;\;\; 5\end{vmatrix}} \\\frac{148\cdot 5 - (14\cdot 246)}{(-2\cdot 5)-(14\cdot 3)} =\frac{-2704}{-52} =52\\\frac{\begin{vmatrix}148 \;\; 14\\ 246\;\;\; 5\end{vmatrix}}{\begin{vmatrix}-2 \;\; 14\\ 3\;\;\; 5\end{vmatrix}} =52[/tex]
The x-value of the solution for the system of equations
[tex]\frac{\begin{vmatrix}148 \;\; 14\\ 246\;\;\; 5\end{vmatrix}}{\begin{vmatrix}-2 \;\; 14\\ 3\;\;\; 5\end{vmatrix}} =52[/tex]
Learn more about Cramer's rule here :
brainly.com/question/15327191
