Solve the System of Equations x^2+4y^2=100 4y-x^2=-20

$x^{2} + 4 y^{2} = 100$ $4 y - x^{2} = - 20$

Step 1

Solve for $y$ in $4 y - x^{2} = - 20$ .

Add $x^{2}$ to both sides of the equation.

$4 y = - 20 + x^{2}$

$x^{2} + 4 y^{2} = 100$

Divide each term in $4 y = - 20 + x^{2}$ by $4$ and simplify.

Divide each term in $4 y = - 20 + x^{2}$ by $4$ .

$\frac{4 y}{4} = \frac{- 20}{4} + \frac{x^{2}}{4}$

$x^{2} + 4 y^{2} = 100$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 20}{4} + \frac{x^{2}}{4}$

$x^{2} + 4 y^{2} = 100$

Divide $y$ by $1$ .

$y = \frac{- 20}{4} + \frac{x^{2}}{4}$

$x^{2} + 4 y^{2} = 100$

$y = \frac{- 20}{4} + \frac{x^{2}}{4}$

$x^{2} + 4 y^{2} = 100$

$y = \frac{- 20}{4} + \frac{x^{2}}{4}$

$x^{2} + 4 y^{2} = 100$

Simplify the right side.

Divide $- 20$ by $4$ .

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 4 y^{2} = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 4 y^{2} = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 4 y^{2} = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 4 y^{2} = 100$

Step 2

Replace all occurrences of $y$ with $- 5 + \frac{x^{2}}{4}$ in each equation.

Replace all occurrences of $y$ in $x^{2} + 4 y^{2} = 100$ with $- 5 + \frac{x^{2}}{4}$ .

$x^{2} + 4 {(- 5 + \frac{x^{2}}{4})}^{2} = 100$

$y = - 5 + \frac{x^{2}}{4}$

Simplify the left side.

Simplify $x^{2} + 4 {(- 5 + \frac{x^{2}}{4})}^{2}$ .

Simplify each term.

Rewrite ${(- 5 + \frac{x^{2}}{4})}^{2}$ as $(- 5 + \frac{x^{2}}{4}) (- 5 + \frac{x^{2}}{4})$ .

$x^{2} + 4 ((- 5 + \frac{x^{2}}{4}) (- 5 + \frac{x^{2}}{4})) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Expand $(- 5 + \frac{x^{2}}{4}) (- 5 + \frac{x^{2}}{4})$ using the FOIL Method.

Apply the distributive property.

$x^{2} + 4 (- 5 (- 5 + \frac{x^{2}}{4}) + \frac{x^{2}}{4} \cdot (- 5 + \frac{x^{2}}{4})) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Apply the distributive property.

$x^{2} + 4 (- 5 \cdot - 5 - 5 \frac{x^{2}}{4} + \frac{x^{2}}{4} \cdot (- 5 + \frac{x^{2}}{4})) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Apply the distributive property.

$x^{2} + 4 (- 5 \cdot - 5 - 5 \frac{x^{2}}{4} + \frac{x^{2}}{4} \cdot - 5 + \frac{x^{2}}{4} \cdot \frac{x^{2}}{4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 4 (- 5 \cdot - 5 - 5 \frac{x^{2}}{4} + \frac{x^{2}}{4} \cdot - 5 + \frac{x^{2}}{4} \cdot \frac{x^{2}}{4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Simplify and combine like terms.

Simplify each term.

Multiply $- 5$ by $- 5$ .

$x^{2} + 4 (25 - 5 \frac{x^{2}}{4} + \frac{x^{2}}{4} \cdot - 5 + \frac{x^{2}}{4} \cdot \frac{x^{2}}{4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Combine $- 5$ and $\frac{x^{2}}{4}$ .

$x^{2} + 4 (25 + \frac{- 5 x^{2}}{4} + \frac{x^{2}}{4} \cdot - 5 + \frac{x^{2}}{4} \cdot \frac{x^{2}}{4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Move the negative in front of the fraction.

$x^{2} + 4 (25 - \frac{(5) x^{2}}{4} + \frac{x^{2}}{4} \cdot - 5 + \frac{x^{2}}{4} \cdot \frac{x^{2}}{4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Combine $\frac{x^{2}}{4}$ and $- 5$ .

$x^{2} + 4 (25 - \frac{5 x^{2}}{4} + \frac{x^{2} \cdot - 5}{4} + \frac{x^{2}}{4} \cdot \frac{x^{2}}{4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Move $- 5$ to the left of $x^{2}$ .

$x^{2} + 4 (25 - \frac{5 x^{2}}{4} + \frac{- 5 \cdot x^{2}}{4} + \frac{x^{2}}{4} \cdot \frac{x^{2}}{4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Move the negative in front of the fraction.

$x^{2} + 4 (25 - \frac{5 x^{2}}{4} - \frac{(5) \cdot x^{2}}{4} + \frac{x^{2}}{4} \cdot \frac{x^{2}}{4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Combine.

$x^{2} + 4 (25 - \frac{5 x^{2}}{4} - \frac{5 x^{2}}{4} + \frac{x^{2} x^{2}}{4 \cdot 4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} + 4 (25 - \frac{5 x^{2}}{4} - \frac{5 x^{2}}{4} + \frac{x^{2 + 2}}{4 \cdot 4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Add $2$ and $2$ .

$x^{2} + 4 (25 - \frac{5 x^{2}}{4} - \frac{5 x^{2}}{4} + \frac{x^{4}}{4 \cdot 4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 4 (25 - \frac{5 x^{2}}{4} - \frac{5 x^{2}}{4} + \frac{x^{4}}{4 \cdot 4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Multiply $4$ by $4$ .

$x^{2} + 4 (25 - \frac{5 x^{2}}{4} - \frac{5 x^{2}}{4} + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 4 (25 - \frac{5 x^{2}}{4} - \frac{5 x^{2}}{4} + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Subtract $\frac{5 x^{2}}{4}$ from $- \frac{5 x^{2}}{4}$ .

$x^{2} + 4 (25 - 2 \frac{5 x^{2}}{4} + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 4 (25 - 2 \frac{5 x^{2}}{4} + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$x^{2} + 4 (25 + 2 (- 1) (\frac{5 x^{2}}{4}) + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Factor $2$ out of $4$ .

$x^{2} + 4 (25 + 2 \cdot (- 1 \frac{5 x^{2}}{2 \cdot 2}) + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Cancel the common factor.

$x^{2} + 4 (25 + 2 \cdot (- 1 \frac{5 x^{2}}{2 \cdot 2}) + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Rewrite the expression.

$x^{2} + 4 (25 - 1 \frac{5 x^{2}}{2} + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 4 (25 - 1 \frac{5 x^{2}}{2} + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Rewrite $- 1 \frac{5 x^{2}}{2}$ as $- \frac{5 x^{2}}{2}$ .

$x^{2} + 4 (25 - \frac{5 x^{2}}{2} + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 4 (25 - \frac{5 x^{2}}{2} + \frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Apply the distributive property.

$x^{2} + 4 \cdot 25 + 4 (- \frac{5 x^{2}}{2}) + 4 (\frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Simplify.

Multiply $4$ by $25$ .

$x^{2} + 100 + 4 (- \frac{5 x^{2}}{2}) + 4 (\frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5 x^{2}}{2}$ into the numerator.

$x^{2} + 100 + 4 (\frac{- 5 x^{2}}{2}) + 4 (\frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Factor $2$ out of $4$ .

$x^{2} + 100 + 2 (2) (\frac{- 5 x^{2}}{2}) + 4 (\frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Cancel the common factor.

$x^{2} + 100 + 2 \cdot (2 (\frac{- 5 x^{2}}{2})) + 4 (\frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Rewrite the expression.

$x^{2} + 100 + 2 (- 5 x^{2}) + 4 (\frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 100 + 2 (- 5 x^{2}) + 4 (\frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Multiply $- 5$ by $2$ .

$x^{2} + 100 - 10 x^{2} + 4 (\frac{x^{4}}{16}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$x^{2} + 100 - 10 x^{2} + 4 (\frac{x^{4}}{4 (4)}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Cancel the common factor.

$x^{2} + 100 - 10 x^{2} + 4 (\frac{x^{4}}{4 \cdot 4}) = 100$

$y = - 5 + \frac{x^{2}}{4}$

Rewrite the expression.

$x^{2} + 100 - 10 x^{2} + \frac{x^{4}}{4} = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 100 - 10 x^{2} + \frac{x^{4}}{4} = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 100 - 10 x^{2} + \frac{x^{4}}{4} = 100$

$y = - 5 + \frac{x^{2}}{4}$

$x^{2} + 100 - 10 x^{2} + \frac{x^{4}}{4} = 100$

$y = - 5 + \frac{x^{2}}{4}$

Subtract $10 x^{2}$ from $x^{2}$ .

$- 9 x^{2} + 100 + \frac{x^{4}}{4} = 100$

$y = - 5 + \frac{x^{2}}{4}$

$- 9 x^{2} + 100 + \frac{x^{4}}{4} = 100$

$y = - 5 + \frac{x^{2}}{4}$

$- 9 x^{2} + 100 + \frac{x^{4}}{4} = 100$

$y = - 5 + \frac{x^{2}}{4}$

$- 9 x^{2} + 100 + \frac{x^{4}}{4} = 100$

$y = - 5 + \frac{x^{2}}{4}$

Step 3

Solve for $x$ in $- 9 x^{2} + 100 + \frac{x^{4}}{4} = 100$ .

Substitute $u = x^{2}$ into the equation. This will make the quadratic formula easy to use.

$\frac{u^{2}}{4} - 9 u + 100 = 100$

$u = x^{2}$

$y = - 5 + \frac{x^{2}}{4}$

Multiply each term in $\frac{u^{2}}{4} - 9 u + 100 = 100$ by $4$ to eliminate the fractions.

Multiply each term in $\frac{u^{2}}{4} - 9 u + 100 = 100$ by $4$ .

$\frac{u^{2}}{4} \cdot 4 - 9 u \cdot 4 + 100 \cdot 4 = 100 \cdot 4$

$y = - 5 + \frac{x^{2}}{4}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{u^{2}}{4} \cdot 4 - 9 u \cdot 4 + 100 \cdot 4 = 100 \cdot 4$

$y = - 5 + \frac{x^{2}}{4}$

Rewrite the expression.

$u^{2} - 9 u \cdot 4 + 100 \cdot 4 = 100 \cdot 4$

$y = - 5 + \frac{x^{2}}{4}$

$u^{2} - 9 u \cdot 4 + 100 \cdot 4 = 100 \cdot 4$

$y = - 5 + \frac{x^{2}}{4}$

Multiply $4$ by $- 9$ .

$u^{2} - 36 u + 100 \cdot 4 = 100 \cdot 4$

$y = - 5 + \frac{x^{2}}{4}$

Multiply $100$ by $4$ .

$u^{2} - 36 u + 400 = 100 \cdot 4$

$y = - 5 + \frac{x^{2}}{4}$

$u^{2} - 36 u + 400 = 100 \cdot 4$

$y = - 5 + \frac{x^{2}}{4}$

$u^{2} - 36 u + 400 = 100 \cdot 4$

$y = - 5 + \frac{x^{2}}{4}$

Simplify the right side.

Multiply $100$ by $4$ .

$u^{2} - 36 u + 400 = 400$

$y = - 5 + \frac{x^{2}}{4}$

$u^{2} - 36 u + 400 = 400$

$y = - 5 + \frac{x^{2}}{4}$

$u^{2} - 36 u + 400 = 400$

$y = - 5 + \frac{x^{2}}{4}$

Subtract $400$ from both sides of the equation.

$u^{2} - 36 u + 400 - 400 = 0$

$y = - 5 + \frac{x^{2}}{4}$

Combine the opposite terms in $u^{2} - 36 u + 400 - 400$ .

Subtract $400$ from $400$ .

$u^{2} - 36 u + 0 = 0$

$y = - 5 + \frac{x^{2}}{4}$

Add $u^{2} - 36 u$ and $0$ .

$u^{2} - 36 u = 0$

$y = - 5 + \frac{x^{2}}{4}$

$u^{2} - 36 u = 0$

$y = - 5 + \frac{x^{2}}{4}$

Factor $u$ out of $u^{2} - 36 u$ .

Factor $u$ out of $u^{2}$ .

$u \cdot u - 36 u = 0$

$y = - 5 + \frac{x^{2}}{4}$

Factor $u$ out of $- 36 u$ .

$u \cdot u + u \cdot - 36 = 0$

$y = - 5 + \frac{x^{2}}{4}$

Factor $u$ out of $u \cdot u + u \cdot - 36$ .

$u (u - 36) = 0$

$y = - 5 + \frac{x^{2}}{4}$

$u (u - 36) = 0$

$y = - 5 + \frac{x^{2}}{4}$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$u = 0$

$u - 36 = 0$

$y = - 5 + \frac{x^{2}}{4}$

Set $u$ equal to $0$ .

$u = 0$

$y = - 5 + \frac{x^{2}}{4}$

Set $u - 36$ equal to $0$ and solve for $u$ .

Set $u - 36$ equal to $0$ .

$u - 36 = 0$

$y = - 5 + \frac{x^{2}}{4}$

Add $36$ to both sides of the equation.

$u = 36$

$y = - 5 + \frac{x^{2}}{4}$

$u = 36$

$y = - 5 + \frac{x^{2}}{4}$

The final solution is all the values that make $u (u - 36) = 0$ true.

$u = 0, 36$

$y = - 5 + \frac{x^{2}}{4}$

Substitute the real value of $u = x^{2}$ back into the solved equation.

$x^{2} = 0$

$x^{2} = 36$

$y = - 5 + \frac{x^{2}}{4}$

Solve the first equation for $x$ .

$x^{2} = 0$

$y = - 5 + \frac{x^{2}}{4}$

Solve the equation for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

$y = - 5 + \frac{x^{2}}{4}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

$y = - 5 + \frac{x^{2}}{4}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

$y = - 5 + \frac{x^{2}}{4}$

Plus or minus $0$ is $0$ .

$x = 0$

$y = - 5 + \frac{x^{2}}{4}$

$x = 0$

$y = - 5 + \frac{x^{2}}{4}$

$x = 0$

$y = - 5 + \frac{x^{2}}{4}$

Solve the second equation for $x$ .

$x^{2} = 36$

$y = - 5 + \frac{x^{2}}{4}$

Solve the equation for $x$ .

Remove parentheses.

$x^{2} = 36$

$y = - 5 + \frac{x^{2}}{4}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{36}$

$y = - 5 + \frac{x^{2}}{4}$

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2}}$

$y = - 5 + \frac{x^{2}}{4}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 6$

$y = - 5 + \frac{x^{2}}{4}$

$x = \pm 6$

$y = - 5 + \frac{x^{2}}{4}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 6$

$y = - 5 + \frac{x^{2}}{4}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 6$

$y = - 5 + \frac{x^{2}}{4}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 6, - 6$

$y = - 5 + \frac{x^{2}}{4}$

$x = 6, - 6$

$y = - 5 + \frac{x^{2}}{4}$

$x = 6, - 6$

$y = - 5 + \frac{x^{2}}{4}$

The solution to $\frac{x^{4}}{4} - 9 x^{2} + 100 = 100$ is $x = 0, 6, - 6$ .

$x = 0, 6, - 6$

$y = - 5 + \frac{x^{2}}{4}$

$x = 0, 6, - 6$

$y = - 5 + \frac{x^{2}}{4}$

Step 4

Replace all occurrences of $x$ with $0$ in each equation.

Replace all occurrences of $x$ in $y = - 5 + \frac{x^{2}}{4}$ with $0$ .

$y = - 5 + \frac{{(0)}^{2}}{4}$

$x = 0$

Simplify the right side.

Simplify $- 5 + \frac{{(0)}^{2}}{4}$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$y = - 5 + \frac{0}{4}$

$x = 0$

Divide $0$ by $4$ .

$y = - 5 + 0$

$x = 0$

$y = - 5 + 0$

$x = 0$

Add $- 5$ and $0$ .

$y = - 5$

$x = 0$

$y = - 5$

$x = 0$

$y = - 5$

$x = 0$

$y = - 5$

$x = 0$

Step 5

Replace all occurrences of $x$ with $6$ in each equation.

Replace all occurrences of $x$ in $y = - 5 + \frac{x^{2}}{4}$ with $6$ .

$y = - 5 + \frac{{(6)}^{2}}{4}$

$x = 6$

Simplify the right side.

Simplify $- 5 + \frac{{(6)}^{2}}{4}$ .

Simplify each term.

Raise $6$ to the power of $2$ .

$y = - 5 + \frac{36}{4}$

$x = 6$

Divide $36$ by $4$ .

$y = - 5 + 9$

$x = 6$

$y = - 5 + 9$

$x = 6$

Add $- 5$ and $9$ .

$y = 4$

$x = 6$

$y = 4$

$x = 6$

$y = 4$

$x = 6$

$y = 4$

$x = 6$

Step 6

Replace all occurrences of $x$ with $0$ in each equation.

Replace all occurrences of $x$ in $y = - 5 + \frac{x^{2}}{4}$ with $0$ .

$y = - 5 + \frac{{(0)}^{2}}{4}$

$x = 0$

Simplify the right side.

Simplify $- 5 + \frac{{(0)}^{2}}{4}$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$y = - 5 + \frac{0}{4}$

$x = 0$

Divide $0$ by $4$ .

$y = - 5 + 0$

$x = 0$

$y = - 5 + 0$

$x = 0$

Add $- 5$ and $0$ .

$y = - 5$

$x = 0$

$y = - 5$

$x = 0$

$y = - 5$

$x = 0$

$y = - 5$

$x = 0$

Step 7

Replace all occurrences of $x$ with $6$ in each equation.

Replace all occurrences of $x$ in $y = - 5 + \frac{x^{2}}{4}$ with $6$ .

$y = - 5 + \frac{{(6)}^{2}}{4}$

$x = 6$

Simplify the right side.

Simplify $- 5 + \frac{{(6)}^{2}}{4}$ .

Simplify each term.

Raise $6$ to the power of $2$ .

$y = - 5 + \frac{36}{4}$

$x = 6$

Divide $36$ by $4$ .

$y = - 5 + 9$

$x = 6$

$y = - 5 + 9$

$x = 6$

Add $- 5$ and $9$ .

$y = 4$

$x = 6$

$y = 4$

$x = 6$

$y = 4$

$x = 6$

$y = 4$

$x = 6$

Step 8

Replace all occurrences of $x$ with $- 6$ in each equation.

Replace all occurrences of $x$ in $y = - 5 + \frac{x^{2}}{4}$ with $- 6$ .

$y = - 5 + \frac{{(- 6)}^{2}}{4}$

$x = - 6$

Simplify the right side.

Simplify $- 5 + \frac{{(- 6)}^{2}}{4}$ .

Simplify each term.

Raise $- 6$ to the power of $2$ .

$y = - 5 + \frac{36}{4}$

$x = - 6$

Divide $36$ by $4$ .

$y = - 5 + 9$

$x = - 6$

$y = - 5 + 9$

$x = - 6$

Add $- 5$ and $9$ .

$y = 4$

$x = - 6$

$y = 4$

$x = - 6$

$y = 4$

$x = - 6$

$y = 4$

$x = - 6$

Step 9

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(0, - 5)$

$(6, 4)$

$(- 6, 4)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(0, - 5), (6, 4), (- 6, 4)$

Equation Form:

$x = 0, y = - 5$

$x = 6, y = 4$

$x = - 6, y = 4$

Step 11

Solve the System of Equations x^2+4y^2=100 4y-x^2=-20

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