Question

Find x, y satisfying the matrix equations

`x[[2],[1]]+y[[3],[5]]+[[-8],[-11]]=0`

Answer 1

Given: 

`x[[2],[1]]+y[[3],[5]]+[[-8],[-11]]=0`

`⇒ [[2x + 3y -8],[x + 5y -11]]=[[0],[0]]`

⇒2x+3y−8=0

⇒2x+3y=8               ...(1)

Also,

x+5y−11=0

⇒x+5y=11

⇒x=11−5y               ...(2)

Putting the value of x in (1), we get

2(11−5y)+3y=8

⇒22−10y+3y=8

⇒−7y=8−22

⇒−7y=−14

⇒y=2

Putting the value of y in (2), we get

x=11−5(2)

⇒x=11−10

⇒x=1

∴ x=1 and y=2