Solve 2x^3y=60; x y=30

Question

Solve the system of equations

(x_{1}, y_{1}) = (- 1, - 30) (x_{2}, y_{2}) = (1, 30)

Evaluate

{2 x^{3} y = 60 x y = 30

Solve the equation for x

More Steps

{2 x^{3} y = 60 x = \frac{30}{y}

Substitute the given value of x into the equation 2 x^{3} y = 60

2 (\frac{30}{y})^{3} y = 60

Simplify

More Steps

\frac{54000}{y ^{2}} = 60

Cross multiply

54000 = y^{2} \times 60

Simplify the equation

54000 = 60 y^{2}

Rewrite the expression

60 \times 900 = 60 y^{2}

Evaluate

900 = y^{2}

Swap the sides of the equation

y^{2} = 900

Take the root of both sides of the equation and remember to use both positive and negative roots

y = \pm 900

Simplify the expression

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y = \pm 30

Separate the equation into 2 possible cases

y = 30 \cup y = - 30

Rearrange the terms

{x = \frac{30}{y} y = 30 \cup {x = \frac{30}{y} y = - 30

Calculate

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{x = 1 y = 30 \cup {x = \frac{30}{y} y = - 30

Calculate

More Steps

{x = 1 y = 30 \cup {x = - 1 y = - 30

Calculate

{x = - 1 y = - 30 \cup {x = 1 y = 30

Check the solution

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{x = - 1 y = - 30 \cup {x = 1 y = 30

Check the solution

More Steps

{x = - 1 y = - 30 \cup {x = 1 y = 30

Solution

(x_{1}, y_{1}) = (- 1, - 30) (x_{2}, y_{2}) = (1, 30)

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