Solve {l}{x+7y+3z=29}{3z+x-2y=-7}{5y=10-2x}

$$\left. \begin{array} { l } { x + 7 y + 3 z = 29 } \\ { 3 z + x - 2 y = - 7 } \\ { 5 y = 10 - 2 x } \end{array} \right.$$

Solve for x, y, z

$$x=-5$$

$$y=4$$

$$z=2$$

Short Steps Using Substitution

Solve x+7y+3z=29 for x.

$$x=-7y-3z+29$$

Substitute -7y-3z+29 for x in the second and third equation.

$$3z-7y-3z+29-2y=-7 5y=10-2\left(-7y-3z+29\right)$$

Solve these equations for y and z respectively.

$$y=4 z=8-\frac{3}{2}y$$

Substitute 4 for y in the equation z=8-\frac{3}{2}y.

$$z=8-\frac{3}{2}\times 4$$

Calculate z from z=8-\frac{3}{2}\times 4.

$$z=2$$

Substitute 4 for y and 2 for z in the equation x=-7y-3z+29.

$$x=-7\times 4-3\times 2+29$$

Calculate x from x=-7\times 4-3\times 2+29.

$$x=-5$$

The system is now solved.

$$x=-5 y=4 z=2$$