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

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

Solve for x

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

Steps for Solving Linear Equation

Subtract \frac{2}{3}y from both sides.

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

The equation is in standard form.

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

Multiply both sides by 2.

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

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

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

Divide 2-\frac{2y}{3} by \frac{1}{2} by multiplying 2-\frac{2y}{3} by the reciprocal of \frac{1}{2}.

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

Solve for y

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

Steps for Solving Linear Equation

Subtract \frac{1}{2}x from both sides.

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

The equation is in standard form.

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

Divide both sides of the equation by \frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

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

Dividing by \frac{2}{3} undoes the multiplication by \frac{2}{3}.

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

Divide 2-\frac{x}{2} by \frac{2}{3} by multiplying 2-\frac{x}{2} by the reciprocal of \frac{2}{3}.

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