Please help me with this simultaneous equations question!!?

Question

I am completely stuck on the following simultaneous equations problem:

4m - 3n = 10
2m + 3n = -4

Please help me!! It has to be done by tomorrow!! Thank you!

Answer 1

There are a couple of ways of doing it.

The easiest way is to add the two equations together. So you get:

4m - 3n = 10
2m + 3n = -4
------------------
6m + 0n = 6

You get m = 1. You can plug this into either equation (or both if you want to be absolutely sure) to see that n = -2.

And you can usually add equations as long as you can get the terms equal. For example, if you have 2x + 9y = 1 and 7x - 3y = 4, then you can multiply the second equation by 3 so you can add them together.

Another way to solve this is to solve for m or n in either of the equations. You would use some experience to see which is the easiest way of doing this. For example, I would solve for m in the first equation.
4m - 3n = 10
4m = 10 + 3n
m = (10 + 3n)/4

You can plug this into the other equation to solve for n. You would get:
2(10+3n)/4 + 3n = -4
5 + 6n/4 + 3n = -4
18n = -36
n = -2

Obviously, in this case, adding the two equations is better.

Answer 2

Add the equations:

4m - 3n = 10
2m + 3n = -4
__________

6m = 6
m = 1

Then substitute m = 1 into the first equation:

4(1) - 3n = 10
4 - 3n = 10
- 3n = 6
n = -2

Then check if it works by substituting into the second equation

2(1) + 3(-2) = 2 - 6 = -4 so it works.

Answer 3

Substitution method: Take the first equation, solve for one variable in terms of the other (say, solve for m in terms of n), and substitute into the second equation.

4m - 3n = 10
4m = 10 + 3n
m = (10 + 3n) / 4

Now substitute this for "m" in the second equation:

2m + 3n = -4
2(10 + 3n)/4 + 3n = -4
(10 + 3n)/2 + 3n = -4
5 + (3/2)n + 3n = -4
(3/2)n + 3n = -4 - 5
(3/2)n + (6/2)n = -9
(9/2)n = -9
n = -9*(2/9)
n = -2.

So that's n... now to find m, go back to the equation where you have m = stuff and plug in "n = -2":

m = (10 + 3n) / 4
m = (10 + 3(-2)) / 4
m = (10 - 6) / 4
m = 4 / 4
m = 1

Check:

4(1) - 3(-2) = 4 + 6 = 10 ./
2(1) + 3(-2) = 2 - 6 = -4 ./

Answer 4

Add the two equations together: this gives 6m = 6, therefore m = 1.

In one of the original equations substitute 1 for m.
In the first equation this would give 4 - 3n = 10. Take away 4 from both sides: -3n = 6. Divide both sides by -3: n = -2.

So the solution is m = 1, n = -2.

Check in the other original equation by substituting 1 for m and -2 for n:
Left hand side = 2 - 6 = -4.
Right hand side = -4
So the answers are correct.

Answer 5

4m - 3n = 10 - - - - - - - Equation 1
2m + 3n = - 4- - - - - - - Equation 2
- - - - - - - - - - -

6m = 6

6m / 6 = 6 / 6

m = 6/6

m = 1

Insert the m value into equation 1

- - - - - - - - - - - -

4m - 3n = 10

4(1) - 3n = 10

4 - 3n - 4 = 10 - 4

- 3n = 6

- 3n / - 3 = 6 / - 3

n = 6 / - 3

n = - 2

Insert the n value into equation 1

- - - - - - - - - - - - - -

Check for equation 1

4m - 3n = 10

4(1) - 3(- 2) = 10

4 - ( - 6) = 10

4 + 6 = 10

10 = 10

- - - - - - - - - -

Check for equation 2

2m + 3n = - 4

2(1) + 3(- 2) = - 4

2 + (- 6) = - 4

2 - 6 = - 4

- 4 = - 4

- - - - - - - - - - - -

Both equations balance

The solution set { 1, - 2 }

- - - - - - - - - - - - -s-

Answer 6

p = a + 5 164 = 8a + 9p replace p = a + 5 into the backside equation - - - - - - - - - - - - - - - - - - - 164 = 8a + 9p 164 = 8a + 9(a + 5) 164 = 8a + 9a + 40 5 The distributive components on the main spectacular side 164 = 17a + 40 5 gathering like words 164 - 40 5 = 17a + 40 5 - 40 5 Subtracting - 40 5 from the two facets of the equation 119 = 17a 119/17 = 17a/17 Dividing the two facets of the equation by potential of 17 7 = a Insert the a value into the equation - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - fixing for p P = a + 5 p = 7 + 5 p = 12 Insert the p fee into the equation 164 = 8a + 9p 164 = 8(7) + 9(12) 164 = fifty six +108 164 = 164 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - the respond is: a = 7 p = 12

Answer 7

4m - 3n = 10
2m + 3n = -4

Add the two equations together.

You have

6m = 6
m = 1

Substitute m = 1 in one of the two equations to solve for n.

2m + 3n = -4

2(1) +3n = -4
3n = -6
n = -2
.

Answer 8

Just add all together so that 3n cancels, you get 6m = 6 and m =1. Now plug m into either equation and n = -2.

Answer 9

m=1, n = -2

Answer 10

4m-3n=10
2m+3n=-4
========
6m=6
m=1

4(1)-3n=10
4-3n=10
-3n=6
n=-2

The solution set is (1,-2)

Check:
4(1)-3(-2)=10
4+6=10
10=10

2(1)+3(-2)=-4
2-6=-4
-4=-4