Solve {l}{x+y+z=86}{x=1.5y}{z=1.2x}

$$\left. \begin{array} { l } { x + y + z = 86 } \\ { x = 1.5 y } \\ { z = 1.2 x } \end{array} \right.$$

Solve for x, y, z

$$x=30$$

$$y=20$$

$$z=36$$

Short Steps Using Substitution

Reorder the equations.

$$x=1.5y x+y+z=86 z=1.2x$$

Substitute 1.5y for x in the second and third equation.

$$1.5y+y+z=86 z=1.2\times 1.5y$$

Solve these equations for y and z respectively.

$$y=-0.4z+34.4 z=1.8y$$

Substitute -0.4z+34.4 for y in the equation z=1.8y.

$$z=1.8\left(-0.4z+34.4\right)$$

Solve z=1.8\left(-0.4z+34.4\right) for z.

$$z=36$$

Substitute 36 for z in the equation y=-0.4z+34.4.

$$y=-0.4\times 36+34.4$$

Calculate y from y=-0.4\times 36+34.4.

$$y=20$$

Substitute 20 for y in the equation x=1.5y.

$$x=1.5\times 20$$

Calculate x from x=1.5\times 20.

$$x=30$$

The system is now solved.

$$x=30 y=20 z=36$$