Elimination method:
4m = n + 7
3m + 4n + 9 = 0
First, let's get the equations in the same form.
4m - n - 7 = 0
3m + 4n + 9 = 0
Now let's make multiply the first equation by 4 so we can eliminate n.
16m - 4n - 28 = 0
+3m + 4n + 9 = 0
Now we can add the equations.
16m + 3m - 4n + 4n - 28 + 9 = 0
19m + 0n - 19 = 0
19m - 19 = 0
19m = 19
m = 1
Now we put m back into one (or both) of the original equations.
4(1) = n + 7
4 = n + 7
n = -3
If you plug m into the other equation, you get the same result.
Substitution method:
4m = n + 7
3m + 4n + 9 = 0
With this method, we plug one of the equations into the other one. I'm going to use m in the second equation as a substitute for m in the second equation.
3m + 4n + 9 = 0
3m = -4n - 9
m = (-4/3)n - 3
Now I can substitute the right side into the first equation like so:
4[(-4/3)n - 3] = n + 7
(-16n)/3 - 12 = n + 7
(-16n)/3 = n + 19
-16n = 3(n + 19)
-16n = 3n + 57
0 = 16n + 3n + 57
0 = 19n + 57
0 = 19n/19 + 57/19
0 = n + 3
-3 = n
And then we put that back into one of the original equations.
4m = n + 7
4m = -3 + 7
4m = 4
m = 1
Hopefully you learned something from this.
