Solve the following system of equations
-m+2n=9
4m=-3n-14

This is beautiful.

-m+2n=9  (i)
4m=3n-14 (ii)

We are going to use elimination method. Rearrange the equations so that the m and n are on same vertical sides.

-m+2n=9       (i)    (multiply by 4)
4m -3n=-14 (ii)   

We multiply both sides of equation i by 4, because of the 4 attached to the m in equation (ii)

4*(-m+2n)=4*(9) (i)

-4m + 8n = 36 (iii)

Add equations (ii) and (iii)

4m+(-4m) -3n+8n = -14 +36
4m-4m +5n = 22
5n = 22
Divide both sides by 5.

 n = 22/5 = 4.4.

Now let us solve for m.

From:

-m+2n=9  (i)  Let us substitute the solved value of n = 4.4

-m + 2(4.4)  = 9
-m =  9 - 8.8
-m  =   0.2
Multiply both sides by -1.

m = -0.2

Therefore m = -0.2, n = 4.4.

Hurray!