Question

Solve the given system by substitution.
n=5m
n=2/3 m-13

Answer 1

n = -15 and m = -3

Explanation:

To solve the given system of equation, we will follow the steps below:

n = 5m ----------------------------------------------------------------------------(1)

n =
`(2)/(3) m -13` ---------------------------------------------------------------------(2)

substitute for n= 5m in equation (2)

5m =
`(2)/(3) m -13`

subtract
`(2)/(3) m` from both-side of the equation

5m -
`(2)/(3) m` =
`(2)/(3) m` -
`(2)/(3) m -13`

At the right-hand side of the equation
`(2)/(3) m` will cancel-out leaving us with just -13

5m -
`(2)/(3) m` = -13

`(15m - 2m )/(3)` = -13

`(13m)/(3)` = -13

multiply both-side of the equation by 3

3 ×
`(13m)/(3)` = -13 × 3

At the left-hand side of the equation 3 will cancel-out 3 leaving is with just 13m

13m = -39

Divide both-side of the equation by 13

13m/13 = -39/13

m = -3

substitute m = -3 in equation (1)

n = 5m

n = 5 (-3)

n = -15

Therefore, n = -15 and m = -3