Question

A system of equations is shown below: n = 3m + 6 n − 2m = 2 What is the solution, in the form (m, n), to the system of equations? (−4, −6) (−5, −9) (2, 6) (1, 8)

Answer 1

`n=3m+6 \\ n-2m=2 \\ \\ \hbox{substitute 3m+6 for n in the second equation:} \\ 3m+6-2m=2 \\ m+6=2 \\ m=2-6 \\ m=-4 \\ \\ n=3m+6=3 * (-4)+6=-12+6=-6 \\ \\ \boxed{(m,n)=(-4,-6)}`

Answer 2

`(-4,-6)`.

Explanation:

We have been given a system of equations and we are asked to find the solution for given system of equations in the form (m,n).

`n=3m+6...(1)`

`n-2m=2...(2)`

We will use substitution method to solve linear equation. Upon substituting equation (10 in equation (2) we will get,

`3m+6-2m=2`

Combine like terms:

`m+6=2`

`m+6-6=2-6`

`m=-4`

Substituting
`m=-4` in equation (2) we will get,

`n-2* -4=2`

`n+8=2`

`n+8-8=2-8`

`n=-6`

Therefore, the solution for our given system of equation is
`(-4,-6)`.