Solve {l}{y=-10+z}{x=2z}{x+2y=10}

$$\left\{ \begin{array} { l } { y = - 10 + z } \\ { x = 2 z } \\ { x + 2 y = 10 } \end{array} \right.$$

Solve for y, z, x

$$x=15$$

$$y = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

$$z = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

Short Steps Using Substitution

Substitute -10+z for y in the equation x+2y=10.

$$x+2\left(-10+z\right)=10$$

Solve the second equation for z and the third equation for x.

$$z=\frac{1}{2}x x=30-2z$$

Substitute \frac{1}{2}x for z in the equation x=30-2z.

$$x=30-2\times \frac{1}{2}x$$

Solve x=30-2\times \frac{1}{2}x for x.

$$x=15$$

Substitute 15 for x in the equation z=\frac{1}{2}x.

$$z=\frac{1}{2}\times 15$$

Calculate z from z=\frac{1}{2}\times 15.

$$z=\frac{15}{2}$$

Substitute \frac{15}{2} for z in the equation y=-10+z.

$$y=-10+\frac{15}{2}$$

Calculate y from y=-10+\frac{15}{2}.

$$y=-\frac{5}{2}$$

The system is now solved.

$$y=-\frac{5}{2} z=\frac{15}{2} x=15$$