Answer:
Let's solve the given system of equations step by step.
Equation 1: 1/3(m - 2n) = 2
To eliminate the fraction, we can multiply both sides of the equation by 3:
3 * (1/3)(m - 2n) = 3 * 2
m - 2n = 6
Equation 2: (m + n)/4 = 1/2
To eliminate the fraction, we can multiply both sides of the equation by 4:
4 * \[(m + n)/4\] = 4 * (1/2)
m + n = 2
Now we have two equations:
m - 2n = 6 (Equation 1)
m + n = 2 (Equation 2)
We can solve this system of equations by using the method of substitution or elimination.
Let's solve it by elimination:
Multiply Equation 2 by 2 to make the coefficients of 'm' in both equations equal:
2 * (m + n) = 2 * 2
2m + 2n = 4
Now we can add the equations together to eliminate 'n':
(m - 2n) + (2m + 2n) = 6 + 4
3m = 10
Divide both sides by 3 to solve for 'm':
m = 10/3
Substitute the value of 'm' back into Equation 2 to solve for 'n':
(10/3) + n = 2
Subtract 10/3 from both sides:
n = 2 - 10/3
To simplify the expression for 'n', we need a common denominator:
n = 6/3 - 10/3
n = -4/3
Therefore, the solution to the system of equations is:
m = 10/3
n = -4/3