Solve 3x-5y+4/4+2x-2y+12/8=-2

$$\frac { 3 x - 5 y + 4 } { 4 } + \frac { 2 x - 2 y + 12 } { 8 } = - 2$$

Solve for x

$$x=\frac{3\left(y-3\right)}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 4,8.

$$2\left(3x-5y+4\right)+2x-2y+12=-16$$

Use the distributive property to multiply 2 by 3x-5y+4.

$$6x-10y+8+2x-2y+12=-16$$

Combine 6x and 2x to get 8x.

$$8x-10y+8-2y+12=-16$$

Combine -10y and -2y to get -12y.

$$8x-12y+8+12=-16$$

Add 8 and 12 to get 20.

$$8x-12y+20=-16$$

Add 12y to both sides.

$$8x+20=-16+12y$$

Subtract 20 from both sides.

$$8x=-16+12y-20$$

Subtract 20 from -16 to get -36.

$$8x=-36+12y$$

The equation is in standard form.

$$8x=12y-36$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{12y-36}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{12y-36}{8}$$

Divide -36+12y by 8.

$$x=\frac{3y-9}{2}$$

Solve for y

$$y=\frac{2x}{3}+3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 4,8.

$$2\left(3x-5y+4\right)+2x-2y+12=-16$$

Use the distributive property to multiply 2 by 3x-5y+4.

$$6x-10y+8+2x-2y+12=-16$$

Combine 6x and 2x to get 8x.

$$8x-10y+8-2y+12=-16$$

Combine -10y and -2y to get -12y.

$$8x-12y+8+12=-16$$

Add 8 and 12 to get 20.

$$8x-12y+20=-16$$

Subtract 8x from both sides.

$$-12y+20=-16-8x$$

Subtract 20 from both sides.

$$-12y=-16-8x-20$$

Subtract 20 from -16 to get -36.

$$-12y=-36-8x$$

The equation is in standard form.

$$-12y=-8x-36$$

Divide both sides by -12.

$$\frac{-12y}{-12}=\frac{-8x-36}{-12}$$

Dividing by -12 undoes the multiplication by -12.

$$y=\frac{-8x-36}{-12}$$

Divide -36-8x by -12.

$$y=\frac{2x}{3}+3$$