Solve g_{1}:y=1/2x-2

$$g _ { 1 } : y = \frac { 1 } { 2 } x - 2$$

Solve for g_1

$$g_{1}=\frac{y\left(x-4\right)}{2}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y, the least common multiple of y,2.

$$2g_{1}=\frac{1}{2}x\times 2y+2y\left(-2\right)$$

Multiply \frac{1}{2} and 2 to get 1.

$$2g_{1}=xy+2y\left(-2\right)$$

Multiply 2 and -2 to get -4.

$$2g_{1}=xy-4y$$

Divide both sides by 2.

$$\frac{2g_{1}}{2}=\frac{y\left(x-4\right)}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$g_{1}=\frac{y\left(x-4\right)}{2}$$

Solve for x

$$x=\frac{2g_{1}}{y}+4$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y, the least common multiple of y,2.

$$2g_{1}=\frac{1}{2}x\times 2y+2y\left(-2\right)$$

Multiply \frac{1}{2} and 2 to get 1.

$$2g_{1}=xy+2y\left(-2\right)$$

Multiply 2 and -2 to get -4.

$$2g_{1}=xy-4y$$

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

$$xy-4y=2g_{1}$$

Add 4y to both sides.

$$xy=2g_{1}+4y$$

The equation is in standard form.

$$yx=4y+2g_{1}$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{4y+2g_{1}}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{4y+2g_{1}}{y}$$

Divide 2g_{1}+4y by y.

$$x=\frac{2g_{1}}{y}+4$$