Solve 3(x-3y)-(5x-2y)=10

$$3(x-3y)-(5x-2y)=10$$

Solve for x

$$x=-\frac{7y}{2}-5$$

Steps for Solving Linear Equation

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

$$3x-9y-\left(5x-2y\right)=10$$

To find the opposite of 5x-2y, find the opposite of each term.

$$3x-9y-5x+2y=10$$

Combine 3x and -5x to get -2x.

$$-2x-9y+2y=10$$

Combine -9y and 2y to get -7y.

$$-2x-7y=10$$

Add 7y to both sides.

$$-2x=10+7y$$

The equation is in standard form.

$$-2x=7y+10$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{7y+10}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{7y+10}{-2}$$

Divide 10+7y by -2.

$$x=-\frac{7y}{2}-5$$

Solve for y

$$y=\frac{-2x-10}{7}$$

Steps for Solving Linear Equation

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

$$3x-9y-\left(5x-2y\right)=10$$

To find the opposite of 5x-2y, find the opposite of each term.

$$3x-9y-5x+2y=10$$

Combine 3x and -5x to get -2x.

$$-2x-9y+2y=10$$

Combine -9y and 2y to get -7y.

$$-2x-7y=10$$

Add 2x to both sides.

$$-7y=10+2x$$

The equation is in standard form.

$$-7y=2x+10$$

Divide both sides by -7.

$$\frac{-7y}{-7}=\frac{2x+10}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$y=\frac{2x+10}{-7}$$

Divide 10+2x by -7.

$$y=\frac{-2x-10}{7}$$