Solve x y=4;x-y=11 - ScanMath

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Question

Solve the system of equations

(x_{1}, y_{1}) = (\frac{11 + 137}{2}, \frac{- 11 + 137}{2}) (x_{2}, y_{2}) = (\frac{11 - 137}{2}, - \frac{11 + 137}{2})

Evaluate

{x y = 4 x - y = 11

Solve the equation for x

{x y = 4 x = 11 + y

Substitute the given value of x into the equation x y = 4

(11 + y) y = 4

Simplify

y (11 + y) = 4

Expand the expression

More Steps

11 y + y^{2} = 4

Move the expression to the left side

11 y + y^{2} - 4 = 0

Rewrite in standard form

y^{2} + 11 y - 4 = 0

Substitute a= 1,b= 11 and c= - 4 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{- 11 \pm 1 1 ^{2} - 4 ( - 4 )}{2}

Simplify the expression

More Steps

y = \frac{- 11 \pm 137}{2}

Separate the equation into 2 possible cases

y = \frac{- 11 + 137}{2} y = \frac{- 11 - 137}{2}

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

y = \frac{- 11 + 137}{2} y = - \frac{11 + 137}{2}

Evaluate the logic

y = \frac{- 11 + 137}{2} \cup y = - \frac{11 + 137}{2}

Rearrange the terms

{x = 11 + y y = \frac{- 11 + 137}{2} \cup {x = 11 + y y = - \frac{11 + 137}{2}

Calculate

More Steps

{x = \frac{11 + 137}{2} y = \frac{- 11 + 137}{2} \cup {x = 11 + y y = - \frac{11 + 137}{2}

Calculate

More Steps

{x = \frac{11 + 137}{2} y = \frac{- 11 + 137}{2} \cup {x = \frac{11 - 137}{2} y = - \frac{11 + 137}{2}

Check the solution

More Steps

{x = \frac{11 + 137}{2} y = \frac{- 11 + 137}{2} \cup {x = \frac{11 - 137}{2} y = - \frac{11 + 137}{2}

Check the solution

More Steps

{x = \frac{11 + 137}{2} y = \frac{- 11 + 137}{2} \cup {x = \frac{11 - 137}{2} y = - \frac{11 + 137}{2}

Solution

(x_{1}, y_{1}) = (\frac{11 + 137}{2}, \frac{- 11 + 137}{2}) (x_{2}, y_{2}) = (\frac{11 - 137}{2}, - \frac{11 + 137}{2})

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