Question

Solve the simultaneous Equation using the two methods4m=n +73m+ 4n+9=0​

Answer 1

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.