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

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

Solve for x

$$x=-\frac{9y}{20}+\frac{3}{4}$$

Steps for Solving Linear Equation

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

$$5\times 2x-15y+15=30x-3\times 2y$$

Multiply 5 and 2 to get 10.

$$10x-15y+15=30x-3\times 2y$$

Multiply -3 and 2 to get -6.

$$10x-15y+15=30x-6y$$

Subtract 30x from both sides.

$$10x-15y+15-30x=-6y$$

Combine 10x and -30x to get -20x.

$$-20x-15y+15=-6y$$

Add 15y to both sides.

$$-20x+15=-6y+15y$$

Combine -6y and 15y to get 9y.

$$-20x+15=9y$$

Subtract 15 from both sides.

$$-20x=9y-15$$

Divide both sides by -20.

$$\frac{-20x}{-20}=\frac{9y-15}{-20}$$

Dividing by -20 undoes the multiplication by -20.

$$x=\frac{9y-15}{-20}$$

Divide 9y-15 by -20.

$$x=-\frac{9y}{20}+\frac{3}{4}$$

Solve for y

$$y=-\frac{20x}{9}+\frac{5}{3}$$

Steps for Solving Linear Equation

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

$$5\times 2x-15y+15=30x-3\times 2y$$

Multiply 5 and 2 to get 10.

$$10x-15y+15=30x-3\times 2y$$

Multiply -3 and 2 to get -6.

$$10x-15y+15=30x-6y$$

Add 6y to both sides.

$$10x-15y+15+6y=30x$$

Combine -15y and 6y to get -9y.

$$10x-9y+15=30x$$

Subtract 10x from both sides.

$$-9y+15=30x-10x$$

Combine 30x and -10x to get 20x.

$$-9y+15=20x$$

Subtract 15 from both sides.

$$-9y=20x-15$$

Divide both sides by -9.

$$\frac{-9y}{-9}=\frac{20x-15}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$y=\frac{20x-15}{-9}$$

Divide 20x-15 by -9.

$$y=-\frac{20x}{9}+\frac{5}{3}$$