Solve 16-(y-3x)=12(x-6)+97

$$16 - ( y - 3 x ) = 12 ( x - 6 ) + 97$$

Solve for x

$$x=-\frac{y}{9}-1$$

Steps for Solving Linear Equation

To find the opposite of y-3x, find the opposite of each term.

$$16-y+3x=12\left(x-6\right)+97$$

Use the distributive property to multiply 12 by x-6.

$$16-y+3x=12x-72+97$$

Add -72 and 97 to get 25.

$$16-y+3x=12x+25$$

Subtract 12x from both sides.

$$16-y+3x-12x=25$$

Combine 3x and -12x to get -9x.

$$16-y-9x=25$$

Subtract 16 from both sides.

$$-y-9x=25-16$$

Subtract 16 from 25 to get 9.

$$-y-9x=9$$

Add y to both sides.

$$-9x=9+y$$

The equation is in standard form.

$$-9x=y+9$$

Divide both sides by -9.

$$\frac{-9x}{-9}=\frac{y+9}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$x=\frac{y+9}{-9}$$

Divide 9+y by -9.

$$x=-\frac{y}{9}-1$$

Solve for y

$$y=-9x-9$$

Steps for Solving Linear Equation

To find the opposite of y-3x, find the opposite of each term.

$$16-y+3x=12\left(x-6\right)+97$$

Use the distributive property to multiply 12 by x-6.

$$16-y+3x=12x-72+97$$

Add -72 and 97 to get 25.

$$16-y+3x=12x+25$$

Subtract 16 from both sides.

$$-y+3x=12x+25-16$$

Subtract 16 from 25 to get 9.

$$-y+3x=12x+9$$

Subtract 3x from both sides.

$$-y=12x+9-3x$$

Combine 12x and -3x to get 9x.

$$-y=9x+9$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{9x+9}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{9x+9}{-1}$$

Divide 9+9x by -1.

$$y=-9x-9$$