Solve x(5y/4x-1)+yz=x+y

$$x( \frac{ 5y }{ 4x } -1)+yz=x+y$$

Solve for y

$$y=\frac{8x}{4z+1}$$

$$z\neq -\frac{1}{4}\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4x.

$$x\left(\frac{5y}{4x}-1\right)\times 4x+yz\times 4x=4xx+4xy$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4x}{4x}.

$$x\left(\frac{5y}{4x}-\frac{4x}{4x}\right)\times 4x+yz\times 4x=4xx+4xy$$

Since \frac{5y}{4x} and \frac{4x}{4x} have the same denominator, subtract them by subtracting their numerators.

$$x\times \frac{5y-4x}{4x}\times 4x+yz\times 4x=4xx+4xy$$

Multiply x and x to get x^{2}.

$$x^{2}\times \frac{5y-4x}{4x}\times 4+yz\times 4x=4xx+4xy$$

Express x^{2}\times \frac{5y-4x}{4x} as a single fraction.

$$\frac{x^{2}\left(5y-4x\right)}{4x}\times 4+yz\times 4x=4xx+4xy$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(-4x+5y\right)}{4}\times 4+yz\times 4x=4xx+4xy$$

Express \frac{x\left(-4x+5y\right)}{4}\times 4 as a single fraction.

$$\frac{x\left(-4x+5y\right)\times 4}{4}+yz\times 4x=4xx+4xy$$

Cancel out 4 and 4.

$$x\left(-4x+5y\right)+yz\times 4x=4xx+4xy$$

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

$$-4x^{2}+5xy+yz\times 4x=4xx+4xy$$

Multiply x and x to get x^{2}.

$$-4x^{2}+5xy+yz\times 4x=4x^{2}+4xy$$

Subtract 4xy from both sides.

$$-4x^{2}+5xy+yz\times 4x-4xy=4x^{2}$$

Combine 5xy and -4xy to get xy.

$$-4x^{2}+xy+yz\times 4x=4x^{2}$$

Add 4x^{2} to both sides.

$$xy+yz\times 4x=4x^{2}+4x^{2}$$

Combine 4x^{2} and 4x^{2} to get 8x^{2}.

$$xy+yz\times 4x=8x^{2}$$

Combine all terms containing y.

$$\left(x+z\times 4x\right)y=8x^{2}$$

The equation is in standard form.

$$\left(4xz+x\right)y=8x^{2}$$

Divide both sides by x+4zx.

$$\frac{\left(4xz+x\right)y}{4xz+x}=\frac{8x^{2}}{4xz+x}$$

Dividing by x+4zx undoes the multiplication by x+4zx.

$$y=\frac{8x^{2}}{4xz+x}$$

Divide 8x^{2} by x+4zx.

$$y=\frac{8x}{4z+1}$$

Solve for x

$$x=\frac{y\left(4z+1\right)}{8}$$

$$z\neq -\frac{1}{4}\text{ and }y\neq 0$$