Solve -5(3x-8)+y(-5x-7)=0

$$- 5 ( 3 x - 8 ) + y ( - 5 x - 7 ) = 0$$

Solve for x

$$x=\frac{40-7y}{5\left(y+3\right)}$$

$$y\neq -3$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5 by 3x-8.

$$-15x+40+y\left(-5x-7\right)=0$$

Use the distributive property to multiply y by -5x-7.

$$-15x+40-5yx-7y=0$$

Subtract 40 from both sides. Anything subtracted from zero gives its negation.

$$-15x-5yx-7y=-40$$

Add 7y to both sides.

$$-15x-5yx=-40+7y$$

Combine all terms containing x.

$$\left(-15-5y\right)x=-40+7y$$

The equation is in standard form.

$$\left(-5y-15\right)x=7y-40$$

Divide both sides by -5y-15.

$$\frac{\left(-5y-15\right)x}{-5y-15}=\frac{7y-40}{-5y-15}$$

Dividing by -5y-15 undoes the multiplication by -5y-15.

$$x=\frac{7y-40}{-5y-15}$$

Divide -40+7y by -5y-15.

$$x=-\frac{7y-40}{5\left(y+3\right)}$$

Solve for y

$$y=\frac{5\left(8-3x\right)}{5x+7}$$

$$x\neq -\frac{7}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -5 by 3x-8.

$$-15x+40+y\left(-5x-7\right)=0$$

Use the distributive property to multiply y by -5x-7.

$$-15x+40-5yx-7y=0$$

Add 15x to both sides. Anything plus zero gives itself.

$$40-5yx-7y=15x$$

Subtract 40 from both sides.

$$-5yx-7y=15x-40$$

Combine all terms containing y.

$$\left(-5x-7\right)y=15x-40$$

Divide both sides by -5x-7.

$$\frac{\left(-5x-7\right)y}{-5x-7}=\frac{15x-40}{-5x-7}$$

Dividing by -5x-7 undoes the multiplication by -5x-7.

$$y=\frac{15x-40}{-5x-7}$$

Divide 15x-40 by -5x-7.

$$y=-\frac{5\left(3x-8\right)}{5x+7}$$