Solve 3x^2y=119 y x-3y=11

Question

{3 x^{2} y = 119 y x - 3 y 119 y x - 3 y = 11

Solve the system of equations

(x_{1}, y_{1}) = (\frac{200279347 + 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852}, \frac{155573 - 11 1414 3 ^{2} - 324}{54}) (x_{2}, y_{2}) = (\frac{200279347 - 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852}, \frac{155573 + 11 1414 3 ^{2} - 324}{54})

Evaluate

{3 x^{2} y = 119 y x - 3 y 119 y x - 3 y = 11

Solve the equation for x

More Steps

{3 x^{2} y = 119 y x - 3 y x = \frac{11 + 3 y}{119 y}

Substitute the given value of x into the equation 3 x^{2} y = 119 y x - 3 y

3 (\frac{11 + 3 y}{119 y})^{2} y = 119 y \times \frac{11 + 3 y}{119 y} - 3 y

Simplify

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\frac{3 ( 121 + 66 y + 9 y ^{2} )}{14161 y} = 119 y \times \frac{11 + 3 y}{119 y} - 3 y

Simplify

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\frac{3 ( 121 + 66 y + 9 y ^{2} )}{14161 y} = 11

Cross multiply

3 (121 + 66 y + 9 y^{2}) = 14161 y \times 11

Simplify the equation

3 (121 + 66 y + 9 y^{2}) = 155771 y

Expand the expression

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363 + 198 y + 27 y^{2} = 155771 y

Move the expression to the left side

363 + 198 y + 27 y^{2} - 155771 y = 0

Subtract the terms

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363 - 155573 y + 27 y^{2} = 0

Rewrite in standard form

27 y^{2} - 155573 y + 363 = 0

Substitute a= 27,b= - 155573 and c= 363 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{155573 \pm ( - 155573 ) ^{2} - 4 \times 27 \times 363}{2 \times 27}

Simplify the expression

y = \frac{155573 \pm ( - 155573 ) ^{2} - 4 \times 27 \times 363}{54}

Simplify the expression

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y = \frac{155573 \pm 15557 3 ^{2} - 39204}{54}

Simplify the radical expression

y = \frac{155573 \pm 11 1414 3 ^{2} - 324}{54}

Separate the equation into 2 possible cases

y = \frac{155573 + 11 1414 3 ^{2} - 324}{54} y = \frac{155573 - 11 1414 3 ^{2} - 324}{54}

Evaluate the logic

y = \frac{155573 + 11 1414 3 ^{2} - 324}{54} \cup y = \frac{155573 - 11 1414 3 ^{2} - 324}{54}

Rearrange the terms

{x = \frac{11 + 3 y}{119 y} y = \frac{155573 + 11 1414 3 ^{2} - 324}{54} \cup {x = \frac{11 + 3 y}{119 y} y = \frac{155573 - 11 1414 3 ^{2} - 324}{54}

Calculate

More Steps

{x = \frac{200279347 - 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852} y = \frac{155573 + 11 1414 3 ^{2} - 324}{54} \cup {x = \frac{11 + 3 y}{119 y} y = \frac{155573 - 11 1414 3 ^{2} - 324}{54}

Calculate

More Steps

{x = \frac{200279347 - 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852} y = \frac{155573 + 11 1414 3 ^{2} - 324}{54} \cup {x = \frac{200279347 + 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852} y = \frac{155573 - 11 1414 3 ^{2} - 324}{54}

Calculate

{x = \frac{200279347 + 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852} y = \frac{155573 - 11 1414 3 ^{2} - 324}{54} \cup {x = \frac{200279347 - 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852} y = \frac{155573 + 11 1414 3 ^{2} - 324}{54}

Check the solution

More Steps

{x = \frac{200279347 + 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852} y = \frac{155573 - 11 1414 3 ^{2} - 324}{54} \cup {x = \frac{200279347 - 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852} y = \frac{155573 + 11 1414 3 ^{2} - 324}{54}

Check the solution

More Steps

{x = \frac{200279347 + 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852} y = \frac{155573 - 11 1414 3 ^{2} - 324}{54} \cup {x = \frac{200279347 - 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852} y = \frac{155573 + 11 1414 3 ^{2} - 324}{54}

Solution

(x_{1}, y_{1}) = (\frac{200279347 + 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852}, \frac{155573 - 11 1414 3 ^{2} - 324}{54}) (x_{2}, y_{2}) = (\frac{200279347 - 18 1414 3 ^{2} - 324 - 1414 3 ^{2}}{12852}, \frac{155573 + 11 1414 3 ^{2} - 324}{54})

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