Which ordered pair (m, n) is a solution to the given system of linear equations?

6m-5m=14
2m=2n+-10

a. (–4, –1)
b. (-31/11, -24/11)
c. (–1, –4)
d. (11, –16)

Option (c) is correct.

The ordered pair (-4, -1) is a solution to the given system of linear equations.

Step-by-step explanation:  

given : system of linear equations.

6m - 5n = 14

2m + 2n = - 10

We have to find the solution to the given system of linear equations.

Consider the given  system of linear equations.

6m - 5n = 14      (1)

2m + 2n = - 10   (2)

We solve the given system using elimination method,

multiply equation (2) by 3 , we have,

(2) ⇒ 6m + 6n = - 30  (3)

Subtract equation (1) and (3)  we have,

6m + 6n - (6m - 5n) = - 30 -14

Simplify, we have,

6n + 5n = - 44

11n = - 44

n = - 4

Put n = -4 in (1)  , we have,

6m - 5n = 14   ⇒ 6m - 5(-4) = 14   ⇒ 6m = 14  -20 ⇒ 6m = -6 ⇒ m = -1

Thus, the ordered pair (-4, -1) is a solution to the given system of linear equations.

The answer is C. (-1, -4)

Step-by-step explanation:

Times the bottom equation by 2 then subtract

6m - 5n=14

-6m + 6n= -30

-11n= 44

Then divide

n= -4

Then plug it in any one of the equations

6m - 5(-4)= 14

Multiply

6m + 20 = 14

Then change sign then subtract

6m = 14 - 20

Simplify

6m = -6

Then divide m = -1

C. (-1, -4)

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