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

Answer:

$(-4,-6)$.

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).

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

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

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,

$n-2\times -4=2$

$n+8=2$

$n+8-8=2-8$

$n=-6$

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

Answer 2

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