Remove parentheses.
\[2x,6y=(4,12)\times 2x+32v\times 4\]
Simplify \((4,12)\times 2x\) to \(4,12\times 2x\).
\[2x,6y=(4,12\times 2x)+32v\times 4\]
Simplify \(12\times 2x\) to \(24x\).
\[2x,6y=(4,24x)+32v\times 4\]
Simplify \(32v\times 4\) to \(128v\).
\[2x,6y=(4,24x)+128v\]
Switch sides.
\[(4,24x)+128v=2x,6y\]
Break down the problem into these 2 equations.
\[(4,24x)+128v=2x\]
\[(4,24x)+128v=6y\]
Solve the 1st equation: \((4,24x)+128v=2x\).
Subtract \((4,24x)\) from both sides.
\[128v=2x-(4,24x)\]
Simplify \(2x-(4,24x)\) to \(2x-4,24x\).
\[128v=2x-4,24x\]
Break down the problem into these 2 equations.
\[128v=2x-4\]
\[128v=24x\]
Solve the 1st equation: \(128v=2x-4\).
Divide both sides by \(128\).
\[v=\frac{2x-4}{128}\]
Factor out the common term \(2\).
\[v=\frac{2(x-2)}{128}\]
Simplify \(\frac{2(x-2)}{128}\) to \(\frac{x-2}{64}\).
\[v=\frac{x-2}{64}\]
\[v=\frac{x-2}{64}\]
Solve the 2nd equation: \(128v=24x\).
Divide both sides by \(128\).
\[v=\frac{24x}{128}\]
Simplify \(\frac{24x}{128}\) to \(\frac{3x}{16}\).
\[v=\frac{3x}{16}\]
\[v=\frac{3x}{16}\]
Collect all solutions.
\[v=\frac{x-2}{64},\frac{3x}{16}\]
\[v=\frac{x-2}{64},\frac{3x}{16}\]
Solve the 2nd equation: \((4,24x)+128v=6y\).
Subtract \((4,24x)\) from both sides.
\[128v=6y-(4,24x)\]
Divide both sides by \(128\).
\[v=\frac{6y-(4,24x)}{128}\]
\[v=\frac{6y-(4,24x)}{128}\]
Collect all solutions.
\[v=\frac{x-2}{64},\frac{3x}{16},\frac{6y-(4,24x)}{128}\]
v=(x-2)/64,(3*x)/16,(6*y-(4,24*x))/128
