Question

How do you solve the system of equations `8x + 15y = 85` and `x + y = 8`?

Answer 1

`x=5`
`y=3`

Explanation:

`8x+15y=85`
`x+y=8`
find one of the variables from the second equation: let's use `y` for example... `y=8-x`

substitute that into the first equation, `8x+15(8-x)=85`
now simplify that... `8x+120-15x=85`
add like terms and isolate the `x` coefficient term: `-7x+120=85`
`-7x=-35`
`x=5`

now take `x` value and put it back into the equation you got for `y`: `y=8-(5)=8-5=3`
`\therefore y=3`

Answer 2

`(x,y)to(5,3)`

Explanation:

`8x+15color(red)(y)=85to(1)`

`x+color(red)(y)=8to(2)`

`"from " (2)color(white)(xx) color(red)(y)=8-xto(3)`

`"substitute " color(red)(y)=8-x" into " (1)`

`rArr8x+15(8-x)=85`

.`rArr8x+120-15x=85larr" distributing"`

`rArr-7x+120=85`

`"subtract 120 from both sides"`

`-7xcancel(120)cancel(-120)=85-120`

`rArr-7x=-35`

`"divide both sides by - 7"`

`(cancel(-7) x)/cancel(-7)=(-35)/(-7)`

`rArrx=5`

`"substitute this value into " (3)`

`rArry=8-5=3`

`color(blue)"As a check " "in " (1)`

`(8xx5)+(15xx3)=40+45=85rarr" True"`

`rArr"the point of intersection "=(5,3)`
graph{(y+x-8)(y+8/15x-17/3)=0 [-10, 10, -5, 5]}