Question

Solve the system of equations using either the substitution method or the multiplication/addition method answer: 3x+2y=14 2x-4y=46x+4y=28 2x-4y=4 8x = 32 x = 4 2y = 14 - 12 = 2 y = 1 (x , y) = (4 , 1) question: Check your solution by writing the system as a matrix equation and using the inverse matrix. (how do I do that?)

Answer 1

my question is how do you turn them into a matrixand then doing using the inverse matrix.

Answer 2

\(Ax = B\)
\(x =A^{-1}B\)
\[A = \left[ \begin{matrix} 3 & 2 \\ 2 & 4 \end{matrix} \right]\]\[B = \left[ \begin{matrix} 14 \\ 4 \end{matrix} \right]\]
\[\left[ \begin{matrix} 3 & 2 \\ 2 & 4 \end{matrix} \right] \left[ \begin{matrix} x \\ y \end{matrix} \right] = \left[ \begin{matrix} 14 \\ 4 \end{matrix} \right]\]

Find the inverse of matrix A, then multiply it by matrix B

Answer 3

so do you just do it in reverse sorry im lost :(

Answer 4

how do you find the inverse?

Answer 5

what are your original equations and did you already solve using the substitution method or the multiplication/addition method ? sorry but it is not very easy to understand your post; everything is all pushed together. Do you only need help with checking using the matrix method?

Answer 6

my question is this
Check your solution by writing the system as a matrix equation and using the inverse matrix

Answer 7

i already solve my first question and i got (1,4) and the numbers were 3x+2y=14 and 2x-4y=4

Answer 8

ok thanks

Answer 9

it is not easy huh?

Answer 10

I would have to review matrices

Answer 11

http://www.youtube.com/watch?v=iH3CUVI9S4k is this helpful ?

Answer 12

\(A^{-1} = \dfrac{1}{|A|} \left[ \begin{matrix} d & -b \\ -c & a \end{matrix} \right]\)

Answer 13

same as @Hero and ad-bc is not = 0

Answer 14

is it