How do I solve this out??

Question

asked Mar 18, 2019 10.6k views

1 Answer

Edoardo Vacchi · Answer 1 · 2019-03-23T10:54:36+0000

(x, y) = (7, -5)

It generally works well to follow directions.

The matrix of coefficients is ...

$\left[\begin{array}{cc}2&4\\-5&3\end{array}\right]$

Its inverse is the transpose of the cofactor matrix, divided by the determinant. That is ...

$(1)/(26)\left[\begin{array}{ccc}3&-4\\5&2\end{array}\right]$

So the solution is the product of this and the vector of constants [-6, -50]. That product is ...

... x = (3·(-6) +(-4)(-50))/26 = 7

... y = (5·(-6) +2·(-50))/26 = -5

The solution using inverse matrices is ...

... (x, y) = (7, -5)