Question

Solving with a matrix, once again. Enter the answer as an ordered pair.

4x - 4y = 12
-7x + 4y = -36

All of this confuses me..

Answer 1

if you add the second line to the first, what do you get ?

Answer 2

Should I cancel both of the fours?

Answer 3

yes, that's the point. if you add those two lines you get
4x -7x -4y +4y = 12 - 36

and -4y + 4y = 0
so you have 4x-7x = 12-36

Answer 4

\[A = \left[\begin{matrix}4 & -4 \\ -7 & 4\end{matrix}\right], B = \left[\begin{matrix}12 \\ -36 \end{matrix}\right]\]\[A ^{-1} = 1/12\left[\begin{matrix}-4 & -4 \\ -7 & -4\end{matrix}\right]\]\[A ^{-1} * \left[\begin{matrix}12 \\ -36\end{matrix}\right] = [-16,-19]\]
x = -16
y = -19

Check:
4(-16) - 4(-19) = 12
-7(-16) + 4(19) = -36

Answer 5

To calculate the inverse matrix of a 2 by 2 matrix:
\[K = \left[\begin{matrix}a & b \\ c & d\end{matrix}\right], K ^{-1} = \left[\begin{matrix}d/(ad-bc) & -b/(ad-bc) \\ -c/(ad-bc) & a/(ad-bc)\end{matrix}\right]\]

Answer 6

To obtain the answer you then just multiply the constant matrix B by the inverse matrice of A