Question

How do you find the values of x and y given `[(2y), (x)]=[(x-3), (y+5)]`?

Answer 1

I found `x=7 and y=2`

Explanation:

For the two column matricesto be equal we need that:
`2y=x-3`
`x=y+5`
so we substitute the second into the first for `x`:
`2y=y+5-3`
rearrange:
`y=2`
substitute back into the secnd:
`x=2+5=7`

Answer 2

`x=7" and " y=2`

Explanation:

When 2 matrices are equal then.

`color(blue)"the x-components are equal and the y-components are equal"`

`rArr2y=x-3larr" x-components"`

and `x=y+5larr" y-components"`

Substitute x = y + 5 into the x-components equation.

`rArr2y=y+5-3rArry=2`

`" and " x=2+5=7`