Solve x y=39 x-y=11 - ScanMath

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Type your math problem... x y=39 x-y=11

Question

Solve the system of equations

(x_{1}, y_{1}) = (\frac{11 + 1837}{78}, \frac{- 11 + 1837}{2}) (x_{2}, y_{2}) = (\frac{11 - 1837}{78}, - \frac{11 + 1837}{2})

Evaluate

{x y = 39 x - y 39 x - y = 11

Solve the equation for y

More Steps

{x y = 39 x - y y = - 11 + 39 x

Substitute the given value of y into the equation x y = 39 x - y

x (- 11 + 39 x) = 39 x - (- 11 + 39 x)

Simplify

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x (- 11 + 39 x) = 11

Expand the expression

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- 11 x + 39 x^{2} = 11

Move the expression to the left side

- 11 x + 39 x^{2} - 11 = 0

Rewrite in standard form

39 x^{2} - 11 x - 11 = 0

Substitute a= 39,b= - 11 and c= - 11 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{11 \pm ( - 11 ) ^{2} - 4 \times 39 ( - 11 )}{2 \times 39}

Simplify the expression

x = \frac{11 \pm ( - 11 ) ^{2} - 4 \times 39 ( - 11 )}{78}

Simplify the expression

More Steps

x = \frac{11 \pm 1837}{78}

Separate the equation into 2 possible cases

x = \frac{11 + 1837}{78} x = \frac{11 - 1837}{78}

Evaluate the logic

x = \frac{11 + 1837}{78} \cup x = \frac{11 - 1837}{78}

Rearrange the terms

{x = \frac{11 + 1837}{78} y = - 11 + 39 x \cup {x = \frac{11 - 1837}{78} y = - 11 + 39 x

Calculate

More Steps

{x = \frac{11 + 1837}{78} y = \frac{- 11 + 1837}{2} \cup {x = \frac{11 - 1837}{78} y = - 11 + 39 x

Calculate

More Steps

{x = \frac{11 + 1837}{78} y = \frac{- 11 + 1837}{2} \cup {x = \frac{11 - 1837}{78} y = - \frac{11 + 1837}{2}

Check the solution

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{x = \frac{11 + 1837}{78} y = \frac{- 11 + 1837}{2} \cup {x = \frac{11 - 1837}{78} y = - \frac{11 + 1837}{2}

Check the solution

More Steps

{x = \frac{11 + 1837}{78} y = \frac{- 11 + 1837}{2} \cup {x = \frac{11 - 1837}{78} y = - \frac{11 + 1837}{2}

Solution

(x_{1}, y_{1}) = (\frac{11 + 1837}{78}, \frac{- 11 + 1837}{2}) (x_{2}, y_{2}) = (\frac{11 - 1837}{78}, - \frac{11 + 1837}{2})

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