Solve 2(-2y+x)/3-3y/2+4y=-3/6

$$\frac { 2 ( - 2 y + x ) } { 3 } - \frac { 3 y } { 2 } + 4 y = - \frac { 3 } { 6 }$$

Solve for x

$$x=\frac{-7y-3}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2,6.

$$2\times 2\left(-2y+x\right)-3\times 3y+24y=-3$$

Multiply 2 and 2 to get 4.

$$4\left(-2y+x\right)-3\times 3y+24y=-3$$

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

$$-8y+4x-3\times 3y+24y=-3$$

Multiply -3 and 3 to get -9.

$$-8y+4x-9y+24y=-3$$

Combine -8y and -9y to get -17y.

$$-17y+4x+24y=-3$$

Combine -17y and 24y to get 7y.

$$7y+4x=-3$$

Subtract 7y from both sides.

$$4x=-3-7y$$

The equation is in standard form.

$$4x=-7y-3$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{-7y-3}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{-7y-3}{4}$$

Solve for y

$$y=\frac{-4x-3}{7}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2,6.

$$2\times 2\left(-2y+x\right)-3\times 3y+24y=-3$$

Multiply 2 and 2 to get 4.

$$4\left(-2y+x\right)-3\times 3y+24y=-3$$

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

$$-8y+4x-3\times 3y+24y=-3$$

Multiply -3 and 3 to get -9.

$$-8y+4x-9y+24y=-3$$

Combine -8y and -9y to get -17y.

$$-17y+4x+24y=-3$$

Combine -17y and 24y to get 7y.

$$7y+4x=-3$$

Subtract 4x from both sides.

$$7y=-3-4x$$

The equation is in standard form.

$$7y=-4x-3$$

Divide both sides by 7.

$$\frac{7y}{7}=\frac{-4x-3}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$y=\frac{-4x-3}{7}$$