Solve \left\{ \begin{array} { l } { x^2+y^2=6}\\ { 2x

Question

Solve the system of equations

Solve using the substitution method

Solve using the elimination method

(x_{1}, y_{1}) = (- \frac{30}{3}, - \frac{2 6}{3}) (x_{2}, y_{2}) = (- \frac{30}{3}, \frac{2 6}{3}) (x_{3}, y_{3}) = (\frac{30}{3}, - \frac{2 6}{3}) (x_{4}, y_{4}) = (\frac{30}{3}, \frac{2 6}{3})

Evaluate

{x^{2} + y^{2} = 6 2 x^{2} - y^{2} = 4

Solve the equation for x

More Steps

{x = 6 - y^{2} \cup x = - 6 - y^{2} 2 x^{2} - y^{2} = 4

Evaluate

{x = 6 - y^{2} 2 x^{2} - y^{2} = 4 \cup {x = - 6 - y^{2} 2 x^{2} - y^{2} = 4

Calculate

More Steps

Evaluate

{x = 6 - y^{2} 2 x^{2} - y^{2} = 4

Substitute the given value of x into the equation 2 x^{2} - y^{2} = 4

2 (6 - y^{2})^{2} - y^{2} = 4

Simplify

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12 - 3 y^{2} = 4

Move the constant to the right-hand side and change its sign

- 3 y^{2} = 4 - 12

Subtract the numbers

- 3 y^{2} = - 8

Multiply both sides of the equation by - \frac{1}{3}

- 3 y^{2} (- \frac{1}{3}) = - 8 (- \frac{1}{3})

Multiply the numbers

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- 3 y^{2} (- \frac{1}{3}) = \frac{8}{3}

Cancel out the greatest common factor - 3

y^{2} = \frac{8}{3}

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

y = \pm \frac{8}{3}

Simplify the expression

More Steps

y = \pm \frac{2 6}{3}

Separate the equation into 2 possible cases

y = \frac{2 6}{3} \cup y = - \frac{2 6}{3}

Rearrange the terms

{x = 6 - y^{2} y = \frac{2 6}{3} \cup {x = 6 - y^{2} y = - \frac{2 6}{3}

Calculate

More Steps

{x = \frac{30}{3} y = \frac{2 6}{3} \cup {x = 6 - y^{2} y = - \frac{2 6}{3}

Calculate

More Steps

{x = \frac{30}{3} y = \frac{2 6}{3} \cup {x = \frac{30}{3} y = - \frac{2 6}{3}

Calculate

{x = \frac{30}{3} y = - \frac{2 6}{3} \cup {x = \frac{30}{3} y = \frac{2 6}{3}

{x = \frac{30}{3} y = - \frac{2 6}{3} \cup {x = \frac{30}{3} y = \frac{2 6}{3} \cup {x = - 6 - y^{2} 2 x^{2} - y^{2} = 4

Calculate

More Steps

Evaluate

{x = - 6 - y^{2} 2 x^{2} - y^{2} = 4

Substitute the given value of x into the equation 2 x^{2} - y^{2} = 4

2 (- 6 - y^{2})^{2} - y^{2} = 4

Simplify

More Steps

12 - 3 y^{2} = 4

Move the constant to the right-hand side and change its sign

- 3 y^{2} = 4 - 12

Subtract the numbers

- 3 y^{2} = - 8

Multiply both sides of the equation by - \frac{1}{3}

- 3 y^{2} (- \frac{1}{3}) = - 8 (- \frac{1}{3})

Multiply the numbers

More Steps

- 3 y^{2} (- \frac{1}{3}) = \frac{8}{3}

Cancel out the greatest common factor - 3

y^{2} = \frac{8}{3}

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

y = \pm \frac{8}{3}

Simplify the expression

More Steps

y = \pm \frac{2 6}{3}

Separate the equation into 2 possible cases

y = \frac{2 6}{3} \cup y = - \frac{2 6}{3}

Rearrange the terms

{x = - 6 - y^{2} y = \frac{2 6}{3} \cup {x = - 6 - y^{2} y = - \frac{2 6}{3}

Calculate

More Steps

{x = - \frac{30}{3} y = \frac{2 6}{3} \cup {x = - 6 - y^{2} y = - \frac{2 6}{3}

Calculate

More Steps

{x = - \frac{30}{3} y = \frac{2 6}{3} \cup {x = - \frac{30}{3} y = - \frac{2 6}{3}

Calculate

{x = - \frac{30}{3} y = - \frac{2 6}{3} \cup {x = - \frac{30}{3} y = \frac{2 6}{3}

{x = \frac{30}{3} y = - \frac{2 6}{3} \cup {x = \frac{30}{3} y = \frac{2 6}{3} \cup {x = - \frac{30}{3} y = - \frac{2 6}{3} \cup {x = - \frac{30}{3} y = \frac{2 6}{3}

Rearrange the terms

{x = - \frac{30}{3} y = - \frac{2 6}{3} \cup {x = - \frac{30}{3} y = \frac{2 6}{3} \cup {x = \frac{30}{3} y = - \frac{2 6}{3} \cup {x = \frac{30}{3} y = \frac{2 6}{3}

Check the solution

More Steps

{x = - \frac{30}{3} y = - \frac{2 6}{3} \cup {x = - \frac{30}{3} y = \frac{2 6}{3} \cup {x = \frac{30}{3} y = - \frac{2 6}{3} \cup {x = \frac{30}{3} y = \frac{2 6}{3}

Check the solution

More Steps

{x = - \frac{30}{3} y = - \frac{2 6}{3} \cup {x = - \frac{30}{3} y = \frac{2 6}{3} \cup {x = \frac{30}{3} y = - \frac{2 6}{3} \cup {x = \frac{30}{3} y = \frac{2 6}{3}

Check the solution

More Steps

{x = - \frac{30}{3} y = - \frac{2 6}{3} \cup {x = - \frac{30}{3} y = \frac{2 6}{3} \cup {x = \frac{30}{3} y = - \frac{2 6}{3} \cup {x = \frac{30}{3} y = \frac{2 6}{3}

Check the solution

More Steps

{x = - \frac{30}{3} y = - \frac{2 6}{3} \cup {x = - \frac{30}{3} y = \frac{2 6}{3} \cup {x = \frac{30}{3} y = - \frac{2 6}{3} \cup {x = \frac{30}{3} y = \frac{2 6}{3}

Solution

(x_{1}, y_{1}) = (- \frac{30}{3}, - \frac{2 6}{3}) (x_{2}, y_{2}) = (- \frac{30}{3}, \frac{2 6}{3}) (x_{3}, y_{3}) = (\frac{30}{3}, - \frac{2 6}{3}) (x_{4}, y_{4}) = (\frac{30}{3}, \frac{2 6}{3})

Show Solution

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