Solve -5y+5*(-2/a+1)=-15

$$- 5 y + 5 \cdot ( \frac { - 2 } { a + 1 } ) = - 15$$

Solve for a

$$a=-\frac{y-1}{y-3}$$

$$y\neq 3$$

Steps for Solving Linear Equation

Variable a cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by a+1.

$$-5y\left(a+1\right)+5\left(-2\right)=-15\left(a+1\right)$$

Use the distributive property to multiply -5y by a+1.

$$-5ya-5y+5\left(-2\right)=-15\left(a+1\right)$$

Multiply 5 and -2 to get -10.

$$-5ya-5y-10=-15\left(a+1\right)$$

Use the distributive property to multiply -15 by a+1.

$$-5ya-5y-10=-15a-15$$

Add 15a to both sides.

$$-5ya-5y-10+15a=-15$$

Add 5y to both sides.

$$-5ya-10+15a=-15+5y$$

Add 10 to both sides.

$$-5ya+15a=-15+5y+10$$

Add -15 and 10 to get -5.

$$-5ya+15a=-5+5y$$

Combine all terms containing a.

$$\left(-5y+15\right)a=-5+5y$$

The equation is in standard form.

$$\left(15-5y\right)a=5y-5$$

Divide both sides by -5y+15.

$$\frac{\left(15-5y\right)a}{15-5y}=\frac{5y-5}{15-5y}$$

Dividing by -5y+15 undoes the multiplication by -5y+15.

$$a=\frac{5y-5}{15-5y}$$

Divide -5+5y by -5y+15.

$$a=\frac{y-1}{3-y}$$

Variable a cannot be equal to -1.

$$a=\frac{y-1}{3-y}\text{, }a\neq -1$$

Solve for y

$$y=\frac{3a+1}{a+1}$$

$$a\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a+1.

$$-5y\left(a+1\right)+5\left(-2\right)=-15\left(a+1\right)$$

Use the distributive property to multiply -5y by a+1.

$$-5ya-5y+5\left(-2\right)=-15\left(a+1\right)$$

Multiply 5 and -2 to get -10.

$$-5ya-5y-10=-15\left(a+1\right)$$

Use the distributive property to multiply -15 by a+1.

$$-5ya-5y-10=-15a-15$$

Add 10 to both sides.

$$-5ya-5y=-15a-15+10$$

Add -15 and 10 to get -5.

$$-5ya-5y=-15a-5$$

Combine all terms containing y.

$$\left(-5a-5\right)y=-15a-5$$

Divide both sides by -5a-5.

$$\frac{\left(-5a-5\right)y}{-5a-5}=\frac{-15a-5}{-5a-5}$$

Dividing by -5a-5 undoes the multiplication by -5a-5.

$$y=\frac{-15a-5}{-5a-5}$$

Divide -15a-5 by -5a-5.

$$y=\frac{3a+1}{a+1}$$