Question

A system of equations is shown below: n = 3m + 7 n − 2m = 1 What is the solution, in the form (m, n), to the system of equations? (3, 7) (1, 8) (−3, −2) (−6, −11)

Answer 1

n=3 m+7
n-2 m=1 | -2 m => n=1+2m

n=3 m+7
n=1+2 m

n=n

3m+7=1+2m |-7 and -2m
m = -6

n=1+2m
n=1+2*(-6)
n=-11

(-6,-11)

Answer 2

( m, n) = ( -6 , 11) .

Explanation:

Given : A system of equations is shown below: n = 3m + 7

n − 2m = 1.

To find : What is the solution, in the form (m, n), to the system of equations.

Solution : We have given

n = 3m + 7 ------(1)

n − 2m = 1

We can write it as n = 1 + 2m -----(2)

In equating both equation (1) = (2).

n = n

3m + 7 = 1 +2m.

On subtracting both sides by 2m

3m - 2m + 7 = 1.

m + 7 = 1

On subtracting by 7 both sides

m = 1 - 7.

m = -6.

On plugging the value of m = -6 in equation 1.

n = 3m + 7

n = 3 (-6) + 7.

n = -18 + 7.

n = -11.

Then solution ( m, n) = ( -6 , 11) .

Therefore, ( m, n) = ( -6 , 11) .