Solve (x+7):(y+10)=2:3.quad4x-3(y-1)=0

$$( x + 7 ) : ( y + 10 ) = 2 : 3 . \quad 4 x - 3 ( y - 1 ) = 0$$

Solve for x

$$x=\frac{2y-1}{3}$$

$$y\neq -10$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3\left(y+10\right), the least common multiple of y+10,3.

$$3\left(x+7\right)=2\left(y+10\right)$$

Use the distributive property to multiply 3 by x+7.

$$3x+21=2\left(y+10\right)$$

Use the distributive property to multiply 2 by y+10.

$$3x+21=2y+20$$

Subtract 21 from both sides.

$$3x=2y+20-21$$

Subtract 21 from 20 to get -1.

$$3x=2y-1$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{2y-1}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{2y-1}{3}$$

Solve for y

$$y=\frac{3x+1}{2}$$

$$x\neq -7$$

Steps for Solving Linear Equation

Variable y cannot be equal to -10 since division by zero is not defined. Multiply both sides of the equation by 3\left(y+10\right), the least common multiple of y+10,3.

$$3\left(x+7\right)=2\left(y+10\right)$$

Use the distributive property to multiply 3 by x+7.

$$3x+21=2\left(y+10\right)$$

Use the distributive property to multiply 2 by y+10.

$$3x+21=2y+20$$

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

$$2y+20=3x+21$$

Subtract 20 from both sides.

$$2y=3x+21-20$$

Subtract 20 from 21 to get 1.

$$2y=3x+1$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{3x+1}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{3x+1}{2}$$

Variable y cannot be equal to -10.

$$y=\frac{3x+1}{2}\text{, }y\neq -10$$