Solve {l}{x+300=y}{x+y+z=2000}{10(-x)+.07y+.08z=20}

$$\left. \begin{array} { l } { x + 300 = y } \\ { x + y + z = 2000 } \\ { 10 ( - x ) + .07 y + .08 z = 20 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{13700}{1009} = 13\frac{583}{1009} \approx 13.577799802$$

$$y = \frac{316400}{1009} = 313\frac{583}{1009} \approx 313.577799802$$

$$z = \frac{1687900}{1009} = 1672\frac{852}{1009} \approx 1672.844400396$$

Short Steps Using Substitution

Solve x+300=y for y.

$$y=x+300$$

Substitute x+300 for y in the second and third equation.

$$x+x+300+z=2000 10\left(-x\right)+0.07\left(x+300\right)+0.08z=20$$

Solve these equations for x and z respectively.

$$x=850-\frac{1}{2}z z=124.125x-12.5$$

Substitute 850-\frac{1}{2}z for x in the equation z=124.125x-12.5.

$$z=124.125\left(850-\frac{1}{2}z\right)-12.5$$

Solve z=124.125\left(850-\frac{1}{2}z\right)-12.5 for z.

$$z=\frac{1687900}{1009}$$

Substitute \frac{1687900}{1009} for z in the equation x=850-\frac{1}{2}z.

$$x=850-\frac{1}{2}\times \frac{1687900}{1009}$$

Calculate x from x=850-\frac{1}{2}\times \frac{1687900}{1009}.

$$x=\frac{13700}{1009}$$

Substitute \frac{13700}{1009} for x in the equation y=x+300.

$$y=\frac{13700}{1009}+300$$

Calculate y from y=\frac{13700}{1009}+300.

$$y=\frac{316400}{1009}$$

The system is now solved.

$$x=\frac{13700}{1009} y=\frac{316400}{1009} z=\frac{1687900}{1009}$$