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)

[tex]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 \times (-4)+6=-12+6=-6 \\ \\ \boxed{(m,n)=(-4,-6)}[/tex]

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ApusApus ApusApus · Answer 2 · 2019-05-30T03:13:06+02:00

Answer:

[tex](-4,-6)[/tex].

Step-by-step 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).

[tex]n=3m+6...(1)[/tex]

[tex]n-2m=2...(2)[/tex]

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

[tex]3m+6-2m=2[/tex]

Combine like terms:

[tex]m+6=2[/tex]

[tex]m+6-6=2-6[/tex]

[tex]m=-4[/tex]

Substituting [tex]m=-4[/tex] in equation (2) we will get,

[tex]n-2\times -4=2[/tex]

[tex]n+8=2[/tex]

[tex]n+8-8=2-8[/tex]

[tex]n=-6[/tex]

Therefore, the solution for our given system of equation is [tex](-4,-6)[/tex].