Question

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

Answer 1

Answer:

n = -15         and          m = -3

Step-by-step explanation:

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

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

n = $\frac{2}{3} m -13$ ---------------------------------------------------------------------(2)

substitute for n= 5m in equation (2)

5m =  $\frac{2}{3} m -13$

subtract $\frac{2}{3} m$ from both-side of the equation

5m -  $\frac{2}{3} m$  = $\frac{2}{3} m$ -  $\frac{2}{3} m -13$

At the right-hand side of the equation  $\frac{2}{3} m$  will cancel-out leaving us with just -13

5m -  $\frac{2}{3} m$  = -13

$\frac{15m - 2m }{3}$ = -13

$\frac{13m}{3}$ = -13

multiply both-side of the equation by 3

3 ×  $\frac{13m}{3}$ = -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