Solve x y=1;2x-3y=17 - ScanMath

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Question

Solve the system of equations

(x_{1}, y_{1}) = (\frac{17 + 313}{4}, \frac{- 17 + 313}{6}) (x_{2}, y_{2}) = (\frac{17 - 313}{4}, - \frac{17 + 313}{6})

Evaluate

{x y = 1 2 x - 3 y = 17

Solve the equation for x

More Steps

{x y = 1 x = \frac{17 + 3 y}{2}

Substitute the given value of x into the equation x y = 1

\frac{17 + 3 y}{2} \times y = 1

Simplify

More Steps

\frac{y ( 17 + 3 y )}{2} = 1

Cross multiply

y (17 + 3 y) = 2

Expand the expression

More Steps

17 y + 3 y^{2} = 2

Move the expression to the left side

17 y + 3 y^{2} - 2 = 0

Rewrite in standard form

3 y^{2} + 17 y - 2 = 0

Substitute a= 3,b= 17 and c= - 2 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{- 17 \pm 1 7 ^{2} - 4 \times 3 ( - 2 )}{2 \times 3}

Simplify the expression

y = \frac{- 17 \pm 1 7 ^{2} - 4 \times 3 ( - 2 )}{6}

Simplify the expression

More Steps

y = \frac{- 17 \pm 313}{6}

Separate the equation into 2 possible cases

y = \frac{- 17 + 313}{6} y = \frac{- 17 - 313}{6}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

y = \frac{- 17 + 313}{6} y = - \frac{17 + 313}{6}

Evaluate the logic

y = \frac{- 17 + 313}{6} \cup y = - \frac{17 + 313}{6}

Rearrange the terms

{x = \frac{17 + 3 y}{2} y = \frac{- 17 + 313}{6} \cup {x = \frac{17 + 3 y}{2} y = - \frac{17 + 313}{6}

Calculate

More Steps

{x = \frac{17 + 313}{4} y = \frac{- 17 + 313}{6} \cup {x = \frac{17 + 3 y}{2} y = - \frac{17 + 313}{6}

Calculate

More Steps

{x = \frac{17 + 313}{4} y = \frac{- 17 + 313}{6} \cup {x = \frac{17 - 313}{4} y = - \frac{17 + 313}{6}

Check the solution

More Steps

{x = \frac{17 + 313}{4} y = \frac{- 17 + 313}{6} \cup {x = \frac{17 - 313}{4} y = - \frac{17 + 313}{6}

Check the solution

More Steps

{x = \frac{17 + 313}{4} y = \frac{- 17 + 313}{6} \cup {x = \frac{17 - 313}{4} y = - \frac{17 + 313}{6}

Solution

(x_{1}, y_{1}) = (\frac{17 + 313}{4}, \frac{- 17 + 313}{6}) (x_{2}, y_{2}) = (\frac{17 - 313}{4}, - \frac{17 + 313}{6})

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