What values of 𝑚m and 𝑛n make both of these equations true? 2𝑛2n==𝑚+6m+6𝑛−3𝑚n−3m==33

The given equations are:

1. 2n = m + 6
2. n - 3m = 33

Let's solve these equations step by step:

Step 1: From equation 1, express m in terms of n: m = 2n - 6

Step 2: Substitute m from equation 1 into equation 2: n - 3(2n - 6) = 33 n - 6n + 18 = 33 -5n = 33 - 18 -5n = 15 n = 15 / -5 n = -3

Step 3: Substitute n = -3 into equation 1 to find m: 2(-3) = m + 6 -6 = m + 6 m = -6 - 6 m = -12

So, the values of m and n that make both of these equations true are m = -12 and n = -3.