f) {[(x+y)/(2)-(x-y)/(3)=3],[(x+2y)/(3)-(x-2y)/(4)=3]:}

Write Equations: First, let's write down the system of equations: [(x+y)/(2)-(x-y)/(3)=3], [(x+2y)/(3)-(x-2y)/(4)=3]Solve First Equation: Now, let's solve the first equation for x and y: (x+y)/(2)-(x-y)/(3)=3 To clear the fractions, multiply everything by the least common multiple of 2 and 3, which is 6: 6[(x+y)/(2)] - 6[(x-y)/(3)] = 6*3Simplify First Equation: Simplify the equation: 3(x+y) - 2(x-y) = 18Combine Terms: Distribute the 3 and the 2: 3x + 3y - 2x + 2y = 18Solve Second Equation: Combine like terms: x + 5y = 18Simplify Second Equation: Now, let's solve the second equation for x and y: (x+2y)/(3)-(x-2y)/(4)=3 To clear the fractions, multiply everything by the least common multiple of 3 and 4, which is 12: 12[(x+2y)/(3)] - 12[(x-2y)/(4)] = 12*3Combine Terms: Simplify the equation: 4(x+2y) - 3(x-2y) = 36Distribute the 4 and the 3: 4x + 8y - 3x + 6y = 36Combine like terms: x + 14y = 36 Oops, made a mistake while combining the terms. It should be: x + 14y = 36 should be x + 14y = 36, but I accidentally added the y's wrong. It should be 4x + 8y - 3x - 6y = 36, which simplifies to x + 2y = 36.

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f)
{[(x+y)/(2)-(x-y)/(3)=3],[(x+2y)/(3)-(x-2y)/(4)=3]:}

f) $\left\{\begin{array}{l}\frac{x+y}{2}-\frac{x-y}{3}=3 \\ \frac{x+2 y}{3}-\frac{x-2 y}{4}=3\end{array}\right.$

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Q. f)

\left\{\begin{array}{l}\frac{x+y}{2}-\frac{x-y}{3}=3 \\ \frac{x+2 y}{3}-\frac{x-2 y}{4}=3\end{array}\right.

Write Equations: First, let's write down the system of equations: $\newline$ $\frac{x+y}{2}-\frac{x-y}{3}=3$ , $\frac{x+2y}{3}-\frac{x-2y}{4}=3$
Solve First Equation: Now, let's solve the first equation for $x$ and $y$ : $\frac{x+y}{2}-\frac{x-y}{3}=3$ To clear the fractions, multiply everything by the least common multiple of $2$ and $3$ , which is $6$ : $6\left(\frac{x+y}{2}\right) - 6\left(\frac{x-y}{3}\right) = 6\times 3$
Simplify First Equation: Simplify the equation: $3(x+y) - 2(x-y) = 18$
Combine Terms: Distribute the $3$ and the $2$ : $3x + 3y - 2x + 2y = 18$
Solve Second Equation: Combine like terms: $x + 5y = 18$
Simplify Second Equation: Now, let's solve the second equation for $x$ and $y$ : $\frac{x+2y}{3}-\frac{x-2y}{4}=3$ To clear the fractions, multiply everything by the least common multiple of $3$ and $4$ , which is $12$ : $12\left(\frac{x+2y}{3}\right) - 12\left(\frac{x-2y}{4}\right) = 12\times 3$
Combine Terms: Simplify the equation: $4(x+2y) - 3(x-2y) = 36$
Combine Terms: Simplify the equation: $\newline$ $4(x+2y) - 3(x-2y) = 36$ Distribute the $4$ and the $3$ : $\newline$ $4x + 8y - 3x + 6y = 36$
Combine Terms: Simplify the equation: $\newline$ $4(x+2y) - 3(x-2y) = 36$ Distribute the $4$ and the $3$ : $\newline$ $4x + 8y - 3x + 6y = 36$ Combine like terms: $\newline$ $x + 14y = 36$ $\newline$ Oops, made a mistake while combining the terms. It should be: $\newline$ $x + 14y = 36$ should be $x + 14y = 36$ , but I accidentally added the y's wrong. It should be $4x + 8y - 3x - 6y = 36$ , which simplifies to $x + 2y = 36$ .