Solve the System of @WORD y<3x+5y>3x-1

$y < 3 x + 5 y > 3 x - 1$

Step 1

Solve $y < 3 x + 5 y$ for $y$ .

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

Subtract $5 y$ from both sides of the inequality.

$y - 5 y < 3 x$

Subtract $5 y$ from $y$ .

$- 4 y < 3 x$

Divide each term in $- 4 y < 3 x$ by $- 4$ and simplify.

Divide each term in $- 4 y < 3 x$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} > \frac{3 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} > \frac{3 x}{- 4}$

Divide $y$ by $1$ .

$y > \frac{3 x}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$y > - \frac{3 x}{4}$

Step 2

Solve $3 x + 5 y > 3 x - 1$ for $y$ .

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

Subtract $3 x$ from both sides of the inequality.

$5 y > 3 x - 1 - 3 x$

Combine the opposite terms in $3 x - 1 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$5 y > 0 - 1$

Subtract $1$ from $0$ .

$5 y > - 1$

Divide each term in $5 y > - 1$ by $5$ and simplify.

Divide each term in $5 y > - 1$ by $5$ .

$\frac{5 y}{5} > \frac{- 1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} > \frac{- 1}{5}$

Divide $y$ by $1$ .

$y > \frac{- 1}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y > - \frac{1}{5}$

Step 3

Find the intersection of $y > - \frac{3 x}{4}$ and $y > - \frac{1}{5}$ .

$y > - \frac{3 x}{4}$ and $y > - \frac{1}{5}$

Step 4

Solve the System of @WORD y<3x+5y>3x-1

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