Solve {l}{text{ax}z=3x_{1}+5x_{2}}{text{t.}{l}{x_{1}+x_{1}=4}{2x_{2}+x_{4}=12}{3x_{1}+2x_{2}+x_{1}=18}{x_{1}geq0quad(j=1,*s,5)}}

$$\left. \begin{array} { l } { \text { ax } z = 3 x _ { 1 } + 5 x _ { 2 } } \\ { \text { t. } \left\{ \begin{array} { l } { x _ { 1 } + x _ { 1 } = 4 } \\ { 2 x _ { 2 } + x _ { 4 } = 12 } \\ { 3 x _ { 1 } + 2 x _ { 2 } + x _ { 1 } = 18 } \\ { x _ { 1 } \geq 0 \quad ( j = 1 , \cdots , 5 ) } \end{array} \right.} \end{array} \right.$$

Solve for x_1

$$x_{1}=\frac{z-5x_{2}}{3}$$

Steps for Solving Linear Equation

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

$$3x_{1}+5x_{2}=z$$

Subtract 5x_{2} from both sides.

$$3x_{1}=z-5x_{2}$$

Divide both sides by 3.

$$\frac{3x_{1}}{3}=\frac{z-5x_{2}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x_{1}=\frac{z-5x_{2}}{3}$$