Solve a System of Linear Equations in Two Variables Using Cramer's Rule
-$$\begin{array} { l }
4 x - 2 y = 26 \
4 x + 3 y = 51
\end{array}$$
A) $\{ ( 9,5 ) \}$
B) $\{ ( 5,9 ) \}$
C) $\{ ( - 5,9 ) \}$
D) $\{ ( 9 , - 5 ) \}$

Question

Solve a System of Linear Equations in Two Variables Using Cramer's Rule
-$$\begin{array} { l } 
4 x - 2 y = 26 \
4 x + 3 y = 51
\end{array}$$
A) $\{ ( 9,5 ) \}$
B) $\{ ( 5,9 ) \}$
C) $\{ ( - 5,9 ) \}$
D) $\{ ( 9 , - 5 ) \}$

Quizplus · Accepted Answer

Cramer's Rule uses determinants to solve a system of linear equations. The determinant of the coefficient matrix (D) is calculated from the coefficients of x and y: $$D = \begin{vmatrix} 4 & -2 \ 4 & 3 \end{vmatrix} = (4*3) - (4*(-2)) = 12 + 8 = 20.$$ For x (Dx), replace the x coefficients in the original matrix with the constants from the right side of the equations and calculate the determinant: $$D_x = \begin{vmatrix} 26 & -2 \ 51 & 3 \end{vmatrix} = (26*3) - (51*(-2)) = 78 + 102 = 180.$$ For y (Dy), replace the y coefficients in the original matrix with the constants: $$D_y = \begin{vmatrix} 4 & 26 \ 4 & 51 \end{vmatrix} = (4*51) - (4*26) = 204 - 104 = 100.$$ Solve for x and y: $$x = \frac{D_x}{D} = \frac{180}{20} = 9,$$ $$y = \frac{D_y}{D} = \frac{100}{20} = 5.$$ Therefore, the solution is $\{ ( 9,5 ) \}$.

Solve a System of Linear Equations in Two Variables Using 4x−2y=264x+3y=51\begin{array} { l } 4 x - 2 y = 26 \\4 x + 3 y = 51\end{array}4x−2y=264x+3y=51​

Solve a System of Linear Equations in Two Variables Using $\begin{array} { l } 4 x - 2 y = 26 \\4 x + 3 y = 51\end{array}$