Solve -3left(x-5right)=7left(y-5right)

$$-3 \left( x-5 \right) = 7 \left( y-5 \right)$$

Solve for x

$$x=\frac{50-7y}{3}$$

Steps for Solving Linear Equation

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

$$-3x+15=7\left(y-5\right)$$

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

$$-3x+15=7y-35$$

Subtract 15 from both sides.

$$-3x=7y-35-15$$

Subtract 15 from -35 to get -50.

$$-3x=7y-50$$

Divide both sides by -3.

$$\frac{-3x}{-3}=\frac{7y-50}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$x=\frac{7y-50}{-3}$$

Divide 7y-50 by -3.

$$x=\frac{50-7y}{3}$$

Solve for y

$$y=\frac{50-3x}{7}$$

Steps for Solving Linear Equation

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

$$-3x+15=7\left(y-5\right)$$

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

$$-3x+15=7y-35$$

Swap sides so that all variable terms are on the left hand side.

$$7y-35=-3x+15$$

Add 35 to both sides.

$$7y=-3x+15+35$$

Add 15 and 35 to get 50.

$$7y=-3x+50$$

The equation is in standard form.

$$7y=50-3x$$

Divide both sides by 7.

$$\frac{7y}{7}=\frac{50-3x}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$y=\frac{50-3x}{7}$$