Answer
The solution to this system of equations is $m=4,$ and $n=-3$ or $(4, -3)$.
Work Step by Step
We need to convert the equations so that one variable is the same in both equations, except they have opposite signs. If we add these two equations together, we can eliminate one variable and just deal with one variable instead of two:
It might be easier to get rid of the $m$ terms in both equations, so we want to multiply the first equation by $-3$ and the second equation by $2$ to be able to eliminate the $m$ term:
$(-3)(2m + 4n) = (-3)(10)$
$ (2)(3m + 5n) = (2)(11)$
Multiply to simplify:
$-6m - 12n = -30$
$ 6m + 10n = 22$
Now, we can add the two equations together to come up with one single equation:
$(-6m-12n)+(6m+10m)=-30+22\\
-2n = -8$
Divide each side by $-2$ to solve for $n$:
$n = 4$
Now that we have the value for $n$, we can plug it into one of the equations to solve for $m$.
Let us plug in the value for $n$ into the first equation:
$2m + 4(4) = 10$
$2m + 16 = 10$
Now, we subtract $16$ from both sides of the equation to isolate constants to the right side of the equation:
$2m = -6$
Divide both sides by $2$ to solve for $m$:
$m = -3$
The solution to this system of equations is $m=4,$ and $n=-3$ or $(4, -3)$.
