Solve system of equasions; m/3 + n/3 = 2, 2m + 3n = 10"?

Question

m/3 + n/3 are fractions,

Answer 1

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

3 x (1) : m + n = 6
m = 6 - n ---- (3)

Subst (3) into (2)
2(6-n) + 3n = 10
12 - 2n + 3n = 10
n = -2
m= 8

Answer 2

Hi!

The simplest method to solve this system is the following:

- multiply the first equation by 3:
m/3 + n/3 = 2 |*3 => m + n = 6

- now you write m with respect to n:
m = 6 - n

- the following step is to replace m in the second equation with its expression above:
2*(6 - n) + 3n = 10 => 12 - 2n + 3n = 10

- performing the calculation, you get:
n = 10 - 12 => n = - 2

- now you can compute the value for m, using its relation with n you have written above:
m = 6 - n and n = - 2 => m = 6 - (- 2) => m = 6 + 2 => m = 8 ("-" * "-" = "+")

- now you check if your solution is correct:
8/3 + (- 2)/3 = (8 - 2)/3 = 6/3 = 2 correct
2*8 + 3*(- 2) = 16 - 6 = 10 correct
("+" * "-" = "-")
- your solution is:
m = 8
n = - 2

Good luck at school!

Answer 3

1) m/3 + n/3 = 2
2) 2m + 3n = 10

Multiply equation 1 by 9

3m + 3n = 18

Subtract equation 2 from equation

3m + 3n = 18
2m + 3n = 10
m = 8

Substitute m = 8 back into equation 2 and
solve for n

2m + 3n = 10
2*8 + 3n = 10
3n = -6
n = -2
.

Answer 4

There are many ways to solve this.

I suggest multiplying the first equation through by (-6).

Then, you get:
-2m - 2n = -12
2m + 3n = 10

Add the two together to find:
- 2n + 3n = -12 + 10
n = -2

Then return to the second equation of 2m + 3n = 10, and plug in n = -2.
2m + 3(-2) = 10
m = 8.

Answer 5

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

3 x (1) : m + n = 6
m = 6 - n ---- (3)

Subst (3) into (2)
2(6-n) + 3n = 10
12 - 2n + 3n = 10
n = -2
m= 8

Answer 6

m/3 + n/3 = 2... eq.1
2m + 3n = 10... eq.2

6*eq.1: 2m + 2n = 12
-) eq.2: 2m + 3n = 10
-n = 2
n = -2
from eq.2: 2m + 3n = 10
2m + 3(-2) = 10
2m = 10 + 6
m = 8

ans: n = -2; m = 8

Answer 7

m/3 + n/3 = 2 -------------- {1}

2m + 3n = 10 -------------- {2}

So..........,

{1}*6 - {2}

2m + 2n - 2m - 3n = 12 - 10
(-n) = 2
n = (-2)

subtract the answer of 'n' to (2)

2m + 3(-2) = 10
2m = 10 + 6
2m = 16
m = 8.

So the values are :- [ m = 8; n = (-2) ]

Answer 8

multiply the first equation by -6 and add to the second equation. gives you n= -2, and so m = 8