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

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

Solve for x

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

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{y-x}{3} times \frac{5}{5}. Multiply \frac{2x+y}{5} times \frac{3}{3}.

$$\frac{5\left(y-x\right)}{15}+\frac{3\left(2x+y\right)}{15}=x$$

Since \frac{5\left(y-x\right)}{15} and \frac{3\left(2x+y\right)}{15} have the same denominator, add them by adding their numerators.

$$\frac{5\left(y-x\right)+3\left(2x+y\right)}{15}=x$$

Do the multiplications in 5\left(y-x\right)+3\left(2x+y\right).

$$\frac{5y-5x+6x+3y}{15}=x$$

Combine like terms in 5y-5x+6x+3y.

$$\frac{x+8y}{15}=x$$

Divide each term of x+8y by 15 to get \frac{1}{15}x+\frac{8}{15}y.

$$\frac{1}{15}x+\frac{8}{15}y=x$$

Subtract x from both sides.

$$\frac{1}{15}x+\frac{8}{15}y-x=0$$

Combine \frac{1}{15}x and -x to get -\frac{14}{15}x.

$$-\frac{14}{15}x+\frac{8}{15}y=0$$

Subtract \frac{8}{15}y from both sides. Anything subtracted from zero gives its negation.

$$-\frac{14}{15}x=-\frac{8}{15}y$$

The equation is in standard form.

$$-\frac{14}{15}x=-\frac{8y}{15}$$

Divide both sides of the equation by -\frac{14}{15}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{14}{15}x}{-\frac{14}{15}}=-\frac{\frac{8y}{15}}{-\frac{14}{15}}$$

Dividing by -\frac{14}{15} undoes the multiplication by -\frac{14}{15}.

$$x=-\frac{\frac{8y}{15}}{-\frac{14}{15}}$$

Divide -\frac{8y}{15} by -\frac{14}{15} by multiplying -\frac{8y}{15} by the reciprocal of -\frac{14}{15}.

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

Solve for y

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

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{y-x}{3} times \frac{5}{5}. Multiply \frac{2x+y}{5} times \frac{3}{3}.

$$\frac{5\left(y-x\right)}{15}+\frac{3\left(2x+y\right)}{15}=x$$

Since \frac{5\left(y-x\right)}{15} and \frac{3\left(2x+y\right)}{15} have the same denominator, add them by adding their numerators.

$$\frac{5\left(y-x\right)+3\left(2x+y\right)}{15}=x$$

Do the multiplications in 5\left(y-x\right)+3\left(2x+y\right).

$$\frac{5y-5x+6x+3y}{15}=x$$

Combine like terms in 5y-5x+6x+3y.

$$\frac{x+8y}{15}=x$$

Divide each term of x+8y by 15 to get \frac{1}{15}x+\frac{8}{15}y.

$$\frac{1}{15}x+\frac{8}{15}y=x$$

Subtract \frac{1}{15}x from both sides.

$$\frac{8}{15}y=x-\frac{1}{15}x$$

Combine x and -\frac{1}{15}x to get \frac{14}{15}x.

$$\frac{8}{15}y=\frac{14}{15}x$$

The equation is in standard form.

$$\frac{8}{15}y=\frac{14x}{15}$$

Divide both sides of the equation by \frac{8}{15}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{8}{15}y}{\frac{8}{15}}=\frac{14x}{\frac{8}{15}\times 15}$$

Dividing by \frac{8}{15} undoes the multiplication by \frac{8}{15}.

$$y=\frac{14x}{\frac{8}{15}\times 15}$$

Divide \frac{14x}{15} by \frac{8}{15} by multiplying \frac{14x}{15} by the reciprocal of \frac{8}{15}.

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