Question

Y=x+5 and 4x+y=20?

Answer 1

X=3 and Y=8

Explanation:

I assume that these are two simultaneous equations. The first step is to either solve for `x` or for `y`. I decided to solve for `x` and thus took the second equation:
`4x+y=20` thus `y=20-4x`
Then we can exchange `y` with `"20-4x"` in the first equation to obtain:
`20-4x=x+5`
And then we solve for `x`
`15=5x` thus `x=3`

And from that, we can obviously see that
`3+5=y` and therefore `y=8`, which also checks out with the other equation.

Answer 2

`(x,y)to(3,8)`

Explanation:

`y=x+5to(1)`

`4x+y=20to(2)`

`"substitute "y=x+5" into equation "(2)`

`4x+x+5=20`

`rArr5x+5=20`

`"subtract 5 from both sides"`

`5xcancel(+5)cancel(-5)=20-5`

`rArr5x=15`

`"divide both sides by 5"`

`(cancel(5) x)/cancel(5)=15/5`

`rArrx=3`

`"substitute "x=3" into equation "(1)`

`rArry=3+5=8`

`color(blue)"As a check"`

`"substitute these values into equation "(2)`

`(4xx3)+8=12+8=20to" True"`

`"the point of intersection "=(3,8)`
graph{(y-x+5)(y+4x-20)((x-3)^2+(y-8)^2-0.04)=0 [-20, 20, -10, 10]}