Solve 2x-4y+1/3=-x-3y-6/5

$$\frac{ 2x-4y+1 }{ 3 } = \frac{ -x-3y-6 }{ 5 }$$

Solve for x

$$x=\frac{11y-23}{13}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(2x-4y+1\right)=3\left(-x-3y-6\right)$$

Use the distributive property to multiply 5 by 2x-4y+1.

$$10x-20y+5=3\left(-x-3y-6\right)$$

Use the distributive property to multiply 3 by -x-3y-6.

$$10x-20y+5=3\left(-x\right)-9y-18$$

Subtract 3\left(-x\right) from both sides.

$$10x-20y+5-3\left(-x\right)=-9y-18$$

Multiply -1 and 3 to get -3.

$$10x-20y+5-3\left(-1\right)x=-9y-18$$

Multiply -3 and -1 to get 3.

$$10x-20y+5+3x=-9y-18$$

Combine 10x and 3x to get 13x.

$$13x-20y+5=-9y-18$$

Add 20y to both sides.

$$13x+5=-9y-18+20y$$

Combine -9y and 20y to get 11y.

$$13x+5=11y-18$$

Subtract 5 from both sides.

$$13x=11y-18-5$$

Subtract 5 from -18 to get -23.

$$13x=11y-23$$

Divide both sides by 13.

$$\frac{13x}{13}=\frac{11y-23}{13}$$

Dividing by 13 undoes the multiplication by 13.

$$x=\frac{11y-23}{13}$$

Solve for y

$$y=\frac{13x+23}{11}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(2x-4y+1\right)=3\left(-x-3y-6\right)$$

Use the distributive property to multiply 5 by 2x-4y+1.

$$10x-20y+5=3\left(-x-3y-6\right)$$

Use the distributive property to multiply 3 by -x-3y-6.

$$10x-20y+5=3\left(-x\right)-9y-18$$

Add 9y to both sides.

$$10x-20y+5+9y=3\left(-x\right)-18$$

Combine -20y and 9y to get -11y.

$$10x-11y+5=3\left(-x\right)-18$$

Subtract 10x from both sides.

$$-11y+5=3\left(-x\right)-18-10x$$

Subtract 5 from both sides.

$$-11y=3\left(-x\right)-18-10x-5$$

Subtract 5 from -18 to get -23.

$$-11y=3\left(-x\right)-23-10x$$

Multiply 3 and -1 to get -3.

$$-11y=-3x-23-10x$$

Combine -3x and -10x to get -13x.

$$-11y=-13x-23$$

Divide both sides by -11.

$$\frac{-11y}{-11}=\frac{-13x-23}{-11}$$

Dividing by -11 undoes the multiplication by -11.

$$y=\frac{-13x-23}{-11}$$

Divide -13x-23 by -11.

$$y=\frac{13x+23}{11}$$