\{ \frac { 1 } { x } + \frac { 1 } { y } = \frac { 1 } { 4 }
Solve for x
x=-\frac{4y}{4-y}
y\neq 0\text{ and }y\neq 4
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Quiz
Linear Equation
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\{ \frac { 1 } { x } + \frac { 1 } { y } = \frac { 1 } { 4 }
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4y+4x=xy
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4xy, the least common multiple of x,y,4.
4y+4x-xy=0
Subtract xy from both sides.
4x-xy=-4y
Subtract 4y from both sides. Anything subtracted from zero gives its negation.
\left(4-y\right)x=-4y
Combine all terms containing x.
\frac{\left(4-y\right)x}{4-y}=-\frac{4y}{4-y}
Divide both sides by 4-y.
x=-\frac{4y}{4-y}
Dividing by 4-y undoes the multiplication by 4-y.
x=-\frac{4y}{4-y}\text{, }x\neq 0
Variable x cannot be equal to 0.
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