# Determine x and y such that [[-2,-4,3],[4,4,-4]]  +  [[x-y,-2,-4],[-1,x,-2]] = [[-3,-6,-1],[3,2x+y,-6]]

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to perform the matrix addition to the left side by adding the corresponding members, such that:

`((-2 + x - y,-4 - 2, 3 - 4),(4 - 1, 4 + x, -4 - 2)) = ((-3,-6,-1),(3,2x + y,-6))`

`((-2 + x - y, -6 , -1),(3, 4 + x, -6)) = ((-3,-6,-1),(3,2x + y,-6))`

Equating the corresponding members yields:

`{(-2 + x - y = -3),(4 + x = 2x + y):} => {(x - y = -1),(-x - y = -4):} `

`x - y - x - y = -1 - 4 => -2y = -5 => y = 5/2 => y = 2.5`

`x - 5/2 = -1 => x = -1 + 5/2 => x = 3/2 => x = 1.5`

Hence, evaluating x and y, performing the matrix addition, yields `x = 1.5, y = 2.5.`

rakesh05 | High School Teacher | (Level 1) Assistant Educator

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Given system is `[[-2,-4,3],[4,4,-4]]+[[x-y,-2,-4],[-1,x,-2]]=[[-3,-6,-1],[3,2x+y,-6]]`

Which can be written as

`[[-2+x-y,-4-2,3-4],[4-1,4+x,-4-2]]=[[-3,-6,-1],[3,2x+y,-6]]`

Comparing the similar terms of the matrices on both sides we get

`x-y-2=-3`    and    `4+x=2x+y`

solving the above equations we get ``

`x=3/2`          and   `y=5/2` .