Final answer:
To solve the simultaneous equation, the value of m was 0 and the value of n was -1/2. The equation was simplified step by step and the variables were identified as 'm' and 'n'.
Step-by-step explanation:
Step 1:
Let's simplify the given equation one step at a time.
a)
To solve this simultaneous equation, we need to find the values of 'm' and 'n' that satisfy both equations.
Equation 1: 1/3(m - 3n) = 2m + 2/4
Equation 2: 2m + 2/4 = 1/2
Step 2:
Simplify Equation 1:
Multiply both sides of Equation 1 by 3 to eliminate the fraction: (1/3)(3)(m - 3n) = (3)(2m + 2/4)
m - 3n = 6m + 3/2
-6m + m - 3n - 3/2 = 0
-5m - 3n - 3/2 = 0
-10m - 6n - 3 = 0 (Multiplying the equation by 2 to get rid of a fractional coefficient)
Step 3:
Simplify Equation 2:
Get rid of the fraction by multiplying both sides of Equation 2 by 4: (4)(2m + 2/4) = (4)(1/2)
8m + 2 = 2
8m = 2 - 2
8m = 0
m = 0/8
m = 0
Step 4:
Substitute the value of m into Equation 1 to solve for n:
-10(0) - 6n - 3 = 0
-6n - 3 = 0
-6n = 3
n = 3/-6
n = -1/2
a)
The solution for 'm' is 0 and the solution for 'n' is -1/2.
b)
To solve the simultaneous equation, we simplified the given equation step by step and obtained equations that only contain one variable. We then solved for one variable and substituted the value back into the other equation to find the value of the other variable.
c)
The equation was simplified by multiplying both sides to eliminate the fraction, collecting like terms, and solving for the variables.
d)
The variables involved in the equation are 'm' and 'n'.