Question

Choose the value of the y determinant (Dy) in the following system.

2x + 5y = 7
3x + 5y = 3

Answer 1

do u mean CHOOSE or FIND?

Answer 2

'find', sorry

Answer 3

do you know cramer's rule?

Answer 4

ehh sort of

Answer 5

Okay, so in this case, the regular coefficient matrix would be this:\[\begin{bmatrix}2&5\\3&5\end{bmatrix}\] But we want the y determinant, so we replace the y coefficients with the solution values, to obtain this:\[\begin{bmatrix}2&7\\3&3\end{bmatrix}\]Then we find the determinant in the normal way.

Answer 6

still confused

Answer 7

it is easy
\[ \large y=\frac{|D(y)|}{|A|} \]
where
\[ \large A=\begin{pmatrix}
2 & 5\\ 3 & 5
\end{pmatrix}\qquad\text{and}\qquad
D(y)=\begin{pmatrix}
2 & 7\\ 3 & 3
\end{pmatrix} \]

Answer 8

is the answer -15?

Answer 9

Yes

Answer 10

thanks guys!