Answer to Question #236804 in Algebra for moe

Question

You are given the system of equations

$\begin{array}{ccc}2x & +4y & =10\\ 3x & +2y & =7 \end{array} .$

Which of the following is true about the system above?

1. The determinant of the coefficient matrix is -8
2. With Cramer's rule, the value of x is $x=-\frac{\left| \begin{array}{cc}10 & 4\\ 7 & 2 \end{array} \right |}{8}.​$
3. With Cramer's rule, the value of y is $y=-\frac{\left| \begin{array}{cc}2 & 10\\ 3 & 7 \end{array} \right |}{8}.$
4. The determinant of the coefficient matrix is 8
5. With Cramer's rule, the value of y is $y=\frac{\left| \begin{array}{cc}2 & 10\\ 3 & 7 \end{array} \right |}{8}.$

Answer 1

since the determinant of the coefficient matrix is $\left| {\begin{matrix} 2&4\\ 3&2 \end{matrix}} \right| = 4 - 12 = - 8$ then statement 1 is true. Then then statement 2 and 3 are true and statement 4 and 5 are false.

Answer: 1, 2, 3 are true, 4 and 5 are false