Question

How do you solve the system of equations `2x - 5y = 23` and `y = 4x + 17`?

Answer 1

By arranging and adding the equations `x=-6` and `y=-7`

Explanation:

The first equation is:
`5y=2x-23`
will be added to second equation after arranging it to form:
`-5y=-20x-85`
These two will yield:
`0=-18x-108` or
`18x=-108`
`x=-6`

Now solve y according to known x (for instance first given equation):
`5y=2*(-6)-23`
`5y=-35`
`y=-7`

These are your answers: `x=-6` and `y=-7`

Answer 2

`(-6,-7)`

Explanation:

`2x-5color(red)(y)=23to(1)`

`color(red)(y)=4x+17to(2)`

`"substitute " (2)" into " (1)`

`rArr2x-5(4x+17)=23`

`"distributing "`

`2x-20x-85=23`

`rArr-18x-85=23`

`"add 85 to both sides"`

`-18xcancel(-85)cancel(+85)=23+85`

`rArr-18x=108`

`"divide both sides by - 18"`

`(cancel(-18) x)/cancel(-18)=108/(-18)`

`rArrx=-6`

`"substitute this value into " (2)" and evaluate for y"`

`rArry=(4xx-6)+17=-7`

`color(blue)"As a check"`

`"substitute these values into " (1)" and if true then they are the solution"`

`(2xx-6)-(5xx-7)=-12+35=23=" right side"`

`rArr"point of intersection " =(-6,-7)`
graph{(y-4x-17)(y-2/5x+23/5)=0 [-28.87, 28.86, -14.43, 14.44]}