Solve {l}{text{ise}z=2x_{1}-5x_{2}}{text{to}{l}{-x_{1}+2x_{2}leq4}{x_{1}+x_{2}leq5}{x,ygeq0}}

$$\left. \begin{array} { l } { \text { ise } z = 2 x _ { 1 } - 5 x _ { 2 } } \\ { \text { to } \left\{ \begin{array}{l}{ - x _ { 1 } + 2 x _ { 2 } \leq 4 }\\{ x _ { 1 } + x _ { 2 } \leq 5 }\\{ x , y \geq 0 }\end{array} \right.} \end{array} \right.$$

Solve for x_1

$$x_{1}=\frac{5x_{2}+z}{2}$$

Steps for Solving Linear Equation

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

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

Add 5x_{2} to both sides.

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

The equation is in standard form.

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

Divide both sides by 2.

$$\frac{2x_{1}}{2}=\frac{5x_{2}+z}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x_{1}=\frac{5x_{2}+z}{2}$$