Solve the System of @WORD y<x^2+6y>x^2-4

$y < x^{2} + 6 y > x^{2} - 4$

Step 1

Solve $y < x^{2} + 6 y$ for $y$ .

Move all terms containing $y$ to the left side of the inequality.

Subtract $6 y$ from both sides of the inequality.

$y - 6 y < x^{2}$

Subtract $6 y$ from $y$ .

$- 5 y < x^{2}$

Divide each term in $- 5 y < x^{2}$ by $- 5$ and simplify.

Divide each term in $- 5 y < x^{2}$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 y}{- 5} > \frac{x^{2}}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 y}{- 5} > \frac{x^{2}}{- 5}$

Divide $y$ by $1$ .

$y > \frac{x^{2}}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$y > - \frac{x^{2}}{5}$

Step 2

Solve $x^{2} + 6 y > x^{2} - 4$ for $y$ .

Move all terms not containing $y$ to the right side of the inequality.

Subtract $x^{2}$ from both sides of the inequality.

$6 y > x^{2} - 4 - x^{2}$

Combine the opposite terms in $x^{2} - 4 - x^{2}$ .

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

$6 y > 0 - 4$

Subtract $4$ from $0$ .

$6 y > - 4$

Divide each term in $6 y > - 4$ by $6$ and simplify.

Divide each term in $6 y > - 4$ by $6$ .

$\frac{6 y}{6} > \frac{- 4}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} > \frac{- 4}{6}$

Divide $y$ by $1$ .

$y > \frac{- 4}{6}$

Simplify the right side.

Cancel the common factor of $- 4$ and $6$ .

Factor $2$ out of $- 4$ .

$y > \frac{2 (- 2)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$y > \frac{2 \cdot - 2}{2 \cdot 3}$

Cancel the common factor.

$y > \frac{2 \cdot - 2}{2 \cdot 3}$

Rewrite the expression.

$y > \frac{- 2}{3}$

Move the negative in front of the fraction.

$y > - \frac{2}{3}$

Step 3

Find the intersection of $y > - \frac{x^{2}}{5}$ and $y > - \frac{2}{3}$ .

$y > - \frac{x^{2}}{5}$ and $y > - \frac{2}{3}$

Step 4

Solve the System of @WORD y<x^2+6y>x^2-4

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