Question

3x*3y=3xy

Answer 1

\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{3x\cdot 3y}=3xy\)Calculate the product\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{9y}x=3xy\)Step \(9yx=3xy\)\(9yx=3x\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{y}\)Use the commutative property to reorder the terms\(9yx=3\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{y}x\)Step \(9yx=3yx\)\(9yx=\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{3yx}\)Move the expression to the left-hand side and change its sign \(9yx\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{-3yx}=\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{0}\)Step \(9yx-3yx=0\)\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{9yx-3yx}=0\)Factor out \(x\) from the expression\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{\left(9y-3y\right)x}=0\)Step \(\left(9y-3y\right)x=0\)\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{\left(9y-3y\right)x=0}\)Assume \(9y-3y\ne 0\) and divide both sides of the equation by \(9y-3y\) \(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{x=0,9y-3y\ne 0}\)Step \(x=0,9y-3y\ne 0\)\(x=0,\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{9y-3y}\ne 0\)Rewrite the restriction\(x=0,\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{y}\ne 0\)Solution\(x=0,y\ne 0\)