Solve pm1a+2b+3a=3x1-3

$$\pm 1 a + 2 b + 3 a = 3 x 1 - 3$$

Solve for a (complex solution)

$$a\in \mathrm{C}$$

$$b=\frac{3x_{1}-3}{2}\text{ and }±1+3=0$$

Steps for Solving Linear Equation

Subtract 2b from both sides.

$$\left(±1\right)a+3a=3x_{1}-3-2b$$

Combine all terms containing a.

$$\left(±1+3\right)a=3x_{1}-3-2b$$

The equation is in standard form.

$$\left(±1+3\right)a=3x_{1}-2b-3$$

Divide both sides by ±1+3.

$$\frac{\left(±1+3\right)a}{±1+3}=\frac{3x_{1}-2b-3}{±1+3}$$

Dividing by ±1+3 undoes the multiplication by ±1+3.

$$a=\frac{3x_{1}-2b-3}{±1+3}$$

Solve for a

$$a\in \mathrm{R}$$

$$b=\frac{3x_{1}-3}{2}\text{ and }±1+3=0$$

Steps for Solving Linear Equation

Subtract 2b from both sides.

$$\left(±1\right)a+3a=3x_{1}-3-2b$$

Combine all terms containing a.

$$\left(±1+3\right)a=3x_{1}-3-2b$$

The equation is in standard form.

$$\left(±1+3\right)a=3x_{1}-2b-3$$

Divide both sides by ±1+3.

$$\frac{\left(±1+3\right)a}{±1+3}=\frac{3x_{1}-2b-3}{±1+3}$$

Dividing by ±1+3 undoes the multiplication by ±1+3.

$$a=\frac{3x_{1}-2b-3}{±1+3}$$

Solve for b

$$b=\frac{-a\left(±1\right)+3x_{1}-3a-3}{2}$$

Steps for Solving Linear Equation

Subtract \left(±1\right)a from both sides.

$$2b+3a=3x_{1}-3-\left(±1\right)a$$

Subtract 3a from both sides.

$$2b=3x_{1}-3-\left(±1\right)a-3a$$

Reorder the terms.

$$2b=-a\left(±1\right)-3a+3x_{1}-3$$

The equation is in standard form.

$$2b=-a\left(±1\right)+3x_{1}-3a-3$$

Divide both sides by 2.

$$\frac{2b}{2}=\frac{-a\left(±1\right)+3x_{1}-3a-3}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$b=\frac{-a\left(±1\right)+3x_{1}-3a-3}{2}$$