Question

How do you solve this system of equation: `5x - 6y = 9 and 9- 3y = - x`?

Answer 1

`(x,y)to(9,6)`

Explanation:

`5x-6y=9to(1)`

`9-3y=-xto(2)`

`"rearrange equation "(2)" to give x in terms of y"`

`"multiply through by "-1`

`-9+3y=xto(3)`

`color(blue)"substitute "x=3y-9" into equation "(1)`

`5(3y-9)-6y=9`

`rArr15y-45-6y=9`

`rArr9y-45=9`

`"add 45 to both sides"`

`9ycancel(-45)cancel(+45)=9+45`

`rArr9y=54`

`"divide both sides by 9"`

`(cancel(9) y)/cancel(9)=54/9`

`rArry=6`

`"substitute this value into equation "(3)`

`rArrx=-9+(3xx6)=-9+18=9`

`"point of intersection "=(9,6)`
graph{(y-5/6x+3/2)(y-1/3x-3)((x-9)^2+(x-6)^2-0.05)=0 [-20, 20, -10, 10]}