Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
8x +5y=32
3x - 2y=12
A) Cramer's rule does not apply since $\mathrm { D } = 0 ; \varnothing$
B) $\{ ( 4,0 ) \}$
C) $\{ ( 4,1 ) \}$
D) $\{ ( 3,1 ) \}$

Question

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
8x +5y=32 
3x - 2y=12
A) Cramer's rule does not apply since $\mathrm { D } = 0 ; \varnothing$
B) $\{ ( 4,0 ) \}$
C) $\{ ( 4,1 ) \}$
D) $\{ ( 3,1 ) \}$

Quizplus · Accepted Answer

Cramer's rule can be applied since the determinant $D$ of the coefficient matrix is not zero. By calculating $D_x$ and $D_y$ using the determinants of the modified matrices (replacing the x-column and y-column with the constants, respectively), and then dividing by $D$, we find the solution $x = 4, y = 0$, which corresponds to choice B.

Use Cramer's Rule to Solve the System of Equations D=0;∅\mathrm { D } = 0 ; \varnothingD=0;∅

Use Cramer's Rule to Solve the System of Equations $\mathrm { D } = 0 ; \varnothing$