Given the equations below, what is the value of mn? 2(m + n) + m-9; 3m - 3n =24
To find the value of mn, we can use the given equations:
- 2(m + n) + m - 9 = 0
- 3m - 3n = 24
First, we can simplify equation (2) by dividing both sides by 3:
3m - 3n = 24
Dividing both sides by 3 gives:
m - n = 8
Now, we can solve equation (1) for m in terms of n:
2(m + n) + m - 9 = 0
Distribute the 2 on the left side:
2m + 2n + m - 9 = 0
Combine like terms:
3m + 2n - 9 = 0
Add 9 to both sides:
3m + 2n = 9
Now, we can use the equation m - n = 8 to express m in terms of n:
m = n + 8
Substitute this expression for m into the equation 3m + 2n = 9:
3(n + 8) + 2n = 9
Distribute the 3 on the left side:
3n + 24 + 2n = 9
Combine like terms:
5n + 24 = 9
Subtract 24 from both sides:
5n = 9 - 24 5n = -15
Now, divide both sides by 5 to find n:
n = -15 / 5 n = -3
Now that we have found n, we can find m using m = n + 8:
m = -3 + 8 m = 5
So, the values of m and n are:
m = 5 n = -3
Now, we can find the value of mn:
mn = 5 * (-3) = -15
Therefore, mn = -15.
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