Question

$$(\frac{3x}{4},6)=(9,\frac{y}{6})$$

Answer

x=12,2,(2*y)/9

Solution


Remove parentheses.
\[\frac{3x}{4},6=\frac{3x}{4},6,9,\frac{y}{6}\]
Multiply both sides by \(4,6\).
\[3x=9\times 4,6,\frac{y}{6}\times 4,6\]
Simplify  \(9\times 4\)  to  \(36\).
\[3x=36,6,\frac{y}{6}\times 4,6\]
Simplify  \(\frac{y}{6}\times 4\)  to  \(\frac{2y}{3}\).
\[3x=36,6,\frac{2y}{3},6\]
Break down the problem into these 4 equations.
\[3x=36\]
\[3x=6\]
\[3x=\frac{2y}{3}\]
\[3x=6\]
Solve the 1st equation: \(3x=36\).
\[x=12\]
Solve the 2nd equation: \(3x=6\).
\[x=2\]
Solve the 3rd equation: \(3x=\frac{2y}{3}\).
\[x=\frac{2y}{9}\]
Solve the 4th equation: \(3x=6\).
\[x=2\]
Collect all solutions.
\[x=12,2,\frac{2y}{9}\]