Question

How do you solve the following linear system: `x - 3y = 4x - 13 , y = 1/2x - 3/2`?

Answer 1

`x=3.89" , "y=0.45`

Explanation:

`x-3y=4x-13" (1)"`

`color(red)(y)=1/2 x-3/2" (2)"`

`"rearrange the equation (1) above"`

`x-4x=3y-13`

`-3x=3y-13`

`"divide both sides by 3"`

`(-cancel(3)x)/cancel(3)=(3y-13)/3`

`-x=(cancel(3)y)/cancel(3)-13/3`

`-x=y-13/3`

`color(red)(y)=-x+13/3" (3)"`

`"the equations (3) and (2) are equal"`

`"we can write as ;"`

`1/2x-3/2=-x+13/3`

`1/2x+x=13/3+3/2`

`x/2+color(green)(2/2) x=color(green)(2/2)*13/3+color(green)(3/3)3/2`

`(3x)/2=26/6+9/6`

`(3x)/2=35/6`

`"if "a/b=c/d" then "a*d=b*c`

`3x*6=2*35`

`18x=70`

`x=70/18`

`x=3.89`

`"use (2)"`

`y=1/2x-3/2`

`y=1/2*3.89-3/2`

`y=(3.89-3)/2`

`y=(0.89)/2`

`y=0.45`