Solve 5x-10/3-3y+3/4=x-7y/12

$$\frac { 5 x - 10 } { 3 } - \frac { 3 y + 3 } { 4 } = \frac { x - 7 y } { 12 }$$

Solve for x

$$x=\frac{2y+49}{19}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,12.

$$4\left(5x-10\right)-3\left(3y+3\right)=x-7y$$

Use the distributive property to multiply 4 by 5x-10.

$$20x-40-3\left(3y+3\right)=x-7y$$

Use the distributive property to multiply -3 by 3y+3.

$$20x-40-9y-9=x-7y$$

Subtract 9 from -40 to get -49.

$$20x-49-9y=x-7y$$

Subtract x from both sides.

$$20x-49-9y-x=-7y$$

Combine 20x and -x to get 19x.

$$19x-49-9y=-7y$$

Add 49 to both sides.

$$19x-9y=-7y+49$$

Add 9y to both sides.

$$19x=-7y+49+9y$$

Combine -7y and 9y to get 2y.

$$19x=2y+49$$

Divide both sides by 19.

$$\frac{19x}{19}=\frac{2y+49}{19}$$

Dividing by 19 undoes the multiplication by 19.

$$x=\frac{2y+49}{19}$$

Solve for y

$$y=\frac{19x-49}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,12.

$$4\left(5x-10\right)-3\left(3y+3\right)=x-7y$$

Use the distributive property to multiply 4 by 5x-10.

$$20x-40-3\left(3y+3\right)=x-7y$$

Use the distributive property to multiply -3 by 3y+3.

$$20x-40-9y-9=x-7y$$

Subtract 9 from -40 to get -49.

$$20x-49-9y=x-7y$$

Add 7y to both sides.

$$20x-49-9y+7y=x$$

Combine -9y and 7y to get -2y.

$$20x-49-2y=x$$

Subtract 20x from both sides.

$$-49-2y=x-20x$$

Combine x and -20x to get -19x.

$$-49-2y=-19x$$

Add 49 to both sides.

$$-2y=-19x+49$$

The equation is in standard form.

$$-2y=49-19x$$

Divide both sides by -2.

$$\frac{-2y}{-2}=\frac{49-19x}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$y=\frac{49-19x}{-2}$$

Divide -19x+49 by -2.

$$y=\frac{19x-49}{2}$$