Question

How do you solve the following system?: `1/9x-3/13y=1 , 3/2x - 8y = 2`

Answer 1

`color(blue)(y=-0.25,x=0`

Explanation:

`:.1/9x-3/13y=1`----(1)

`:.3/2x-8y=2`----(2)

multiply `(2) xx 2`

`:.3x-16y=4`

`:.-16y=-3x+4`

`:.16y=3x-4`

`:.color(blue)(y=(3x-4)/16`

substitute `color(blue)(y=(3x-4)/16`--- in `(2)`

`:.3/2x-8((3x-4)/16)=2`

`:.3/2x-(24x+32)/16=2`

multiply both sides by 16

`:.24x-24x+32=32`

`:.24x-24x=32-32`

`:.0=0`

`:.color(blue)(x=0`

substitute `color(blue)(x=0` in `(2)`

`:.3/2(color(blue)0)-8y=2`

`:.-8y=2`

multiply both sides by`-1`

`:.8y=-2`

`:.y=-2/8`

`:.color(blue)(y=-0.25` or `color(blue)( -1/4`

check:

substitute `color(blue)(y=-0.25` in `(2)`

`:.3/2x-8(color(blue)(-0.25))=2`

`:.3/2x+2=2`

`:.3/2x=2-2`

`:.3/2x=0`

`:.color(blue)(x=0`