Use an inverse matrix to solve for x and y

Question

[[5,-4],[4,3]]*[[x],[y]]=[[-6],[-6]]

Answer 1

(x,y) = (38, 49) when you change the 4x to -4x in 2nd equation

otherwise the answer is very messy

easiest solved by graphing the 2 equations

or substitution elimination

or matrix (linear) algebra doing row operations

until you get 1's on the diagonal and 0 elsewhere

then the answer is on the far right column of the augmented matrix

check the answer

5(38) - 4(49) = -6

-4(38) + 3(49) = -5

it works

Answer 2

The inverse matrix is used to solve a system of equations when the system is presented. You have presented a system in matrix form

5x - 4y = -6

4x + 3y = -5.

This system can be solve by substitution or elimination.

Answer 3

Hi Ishwari,

if [A][x]=[B], then [x]=[A^-1][B]:

__ __ -1 __ __ __ __

| 5 4 | *| -6 | = | x |

|__-4 3 __| |__ -6 __| |__ y __|

I'm assuming you can use a calculator. Otherwise the inverse can be found by numerous methods that you should be acquainted with.