Question

Is `(4, 5)` a solution to this system of equations? #20x + y = 11, and 5x + 4y = 18#

Answer 1

No, the solution is `(26/75,61/15) or x=26/75; y=61/15`

Explanation:

Using the two equations to check the given answer (4,5):

`20x+y=11` and then:`5x+4y=18`

`20(4) + 5 != 11` and then: `5(4) + 4(5) !=18`

`80 + 5 !=11` and then: `20 + 20 != 18`

`85 != 11` and then: `40 != 18`

The solution is found here:

`20x+y=11`
`5x+4y=18 to`multiply both sides by `-4`

`cancel(+20x)+y=11`
`cancel(-20x)-16y=-72 to` add

`cancel-15y=cancel-61`

`y=61/15`

`20x+y=11 to` multiply both sides by `4`
`5x+4y=18`

`80xcancel(+4y)=44`
`-5xcancel(-4y)=-18 to` subtract

`75x=26`

`x=26/75`

Using the two equations to check the new answer:

`20x+y=11`
`cancel(20)4(26/(cancel(75)15)) + (61/15)= 11`

`104/15 + 61/15= 11`

`165/15=11`

`11=11`

and then: `5x+4y=18`

`5(26/75) + 4(61/15) =18`

`cancel5(26/(cancel(75)15)) + 244/15= 18`

`270/15 = 18`

`18 = 18`