Solve y=2-7(a-2)/2-(a-2)

$$y = \frac { 2 - 7 ( a - 2 ) } { 2 - ( a - 2 ) }$$

Solve for a

$$a=-\frac{4\left(y-4\right)}{7-y}$$

$$y\neq 7$$

Steps for Solving Linear Equation

Variable a cannot be equal to 4 since division by zero is not defined. Multiply both sides of the equation by -a+4.

$$y\left(-a+4\right)=2-7\left(a-2\right)$$

Use the distributive property to multiply y by -a+4.

$$-ya+4y=2-7\left(a-2\right)$$

Use the distributive property to multiply -7 by a-2.

$$-ya+4y=2-7a+14$$

Add 2 and 14 to get 16.

$$-ya+4y=16-7a$$

Add 7a to both sides.

$$-ya+4y+7a=16$$

Subtract 4y from both sides.

$$-ya+7a=16-4y$$

Combine all terms containing a.

$$\left(-y+7\right)a=16-4y$$

The equation is in standard form.

$$\left(7-y\right)a=16-4y$$

Divide both sides by -y+7.

$$\frac{\left(7-y\right)a}{7-y}=\frac{16-4y}{7-y}$$

Dividing by -y+7 undoes the multiplication by -y+7.

$$a=\frac{16-4y}{7-y}$$

Divide 16-4y by -y+7.

$$a=\frac{4\left(4-y\right)}{7-y}$$

Variable a cannot be equal to 4.

$$a=\frac{4\left(4-y\right)}{7-y}\text{, }a\neq 4$$

Solve for y

$$y=-\frac{7a-16}{4-a}$$

$$a\neq 4$$