Solve for x
x=6+\frac{49}{y}
y\neq 0
Solve for y
y=-\frac{49}{6-x}
x\neq 6
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49=y\left(x-6\right)
Multiply both sides of the equation by 49y, the least common multiple of y,49.
49=yx-6y
Use the distributive property to multiply y by x-6.
yx-6y=49
Swap sides so that all variable terms are on the left hand side.
yx=49+6y
Add 6y to both sides.
yx=6y+49
The equation is in standard form.
\frac{yx}{y}=\frac{6y+49}{y}
Divide both sides by y.
x=\frac{6y+49}{y}
Dividing by y undoes the multiplication by y.
x=6+\frac{49}{y}
Divide 49+6y by y.
49=y\left(x-6\right)
Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 49y, the least common multiple of y,49.
49=yx-6y
Use the distributive property to multiply y by x-6.
yx-6y=49
Swap sides so that all variable terms are on the left hand side.
\left(x-6\right)y=49
Combine all terms containing y.
\frac{\left(x-6\right)y}{x-6}=\frac{49}{x-6}
Divide both sides by x-6.
y=\frac{49}{x-6}
Dividing by x-6 undoes the multiplication by x-6.
y=\frac{49}{x-6}\text{, }y\neq 0
Variable y cannot be equal to 0.
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