We're are given the following system of linear equations:
[tex]n=3m-11[/tex]
[tex]2m+3n=0[/tex]
What we'll do, is substitute the [tex]n[/tex] in the second equation by the definition of [tex]n[/tex] given in the first equation ([tex]n=3m-11[/tex]):
[tex]2m+3n=2m+3(3m-11)=2m+9m-33=11m-33=0[/tex]
We solve for [tex]m[/tex] from the previous equation:
[tex]11m-33=0[/tex]
[tex]m= \frac{33}{11}=3 [/tex]
Now we know [tex]m=3[/tex].
In order to get the numerical value of [tex]n[/tex] we use the fact that [tex]m=3[/tex] in the first equation:
[tex]n=3m-11=3(3)-11=9-11=-2[/tex]
So [tex]n=-2[/tex].
The answer is n=-2 and m=3.
