Solve x y=9 x-y=3 - ScanMath

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Question

Solve the system of equations

(x_{1}, y_{1}) = (\frac{1 + 13}{6}, \frac{- 3 + 3 13}{2}) (x_{2}, y_{2}) = (\frac{1 - 13}{6}, - \frac{3 + 3 13}{2})

Evaluate

{x y = 9 x - y 9 x - y = 3

Solve the equation for y

More Steps

{x y = 9 x - y y = - 3 + 9 x

Substitute the given value of y into the equation x y = 9 x - y

x (- 3 + 9 x) = 9 x - (- 3 + 9 x)

Simplify

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x (- 3 + 9 x) = 3

Expand the expression

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- 3 x + 9 x^{2} = 3

Move the expression to the left side

- 3 x + 9 x^{2} - 3 = 0

Rewrite in standard form

9 x^{2} - 3 x - 3 = 0

Substitute a= 9,b= - 3 and c= - 3 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 9 ( - 3 )}{2 \times 9}

Simplify the expression

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 9 ( - 3 )}{18}

Simplify the expression

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x = \frac{3 \pm 117}{18}

Simplify the radical expression

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x = \frac{3 \pm 3 13}{18}

Separate the equation into 2 possible cases

x = \frac{3 + 3 13}{18} x = \frac{3 - 3 13}{18}

Simplify the expression

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x = \frac{1 + 13}{6} x = \frac{3 - 3 13}{18}

Simplify the expression

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x = \frac{1 + 13}{6} x = \frac{1 - 13}{6}

Evaluate the logic

x = \frac{1 + 13}{6} \cup x = \frac{1 - 13}{6}

Rearrange the terms

{x = \frac{1 + 13}{6} y = - 3 + 9 x \cup {x = \frac{1 - 13}{6} y = - 3 + 9 x

Calculate

More Steps

{x = \frac{1 + 13}{6} y = \frac{- 3 + 3 13}{2} \cup {x = \frac{1 - 13}{6} y = - 3 + 9 x

Calculate

More Steps

{x = \frac{1 + 13}{6} y = \frac{- 3 + 3 13}{2} \cup {x = \frac{1 - 13}{6} y = - \frac{3 + 3 13}{2}

Check the solution

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{x = \frac{1 + 13}{6} y = \frac{- 3 + 3 13}{2} \cup {x = \frac{1 - 13}{6} y = - \frac{3 + 3 13}{2}

Check the solution

More Steps

{x = \frac{1 + 13}{6} y = \frac{- 3 + 3 13}{2} \cup {x = \frac{1 - 13}{6} y = - \frac{3 + 3 13}{2}

Solution

(x_{1}, y_{1}) = (\frac{1 + 13}{6}, \frac{- 3 + 3 13}{2}) (x_{2}, y_{2}) = (\frac{1 - 13}{6}, - \frac{3 + 3 13}{2})

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