Solve {l}{2x-46y=228}{x-4y-6z=49}{-4x-3y+4z=-1}

$$\left\{ \begin{array}{l}{ 2 x - 46 y = 228 }\\{ x - 4 y - 6 z = 49 }\\{ - 4 x - 3 y + 4 z = - 1 }\end{array} \right.$$

Solve for x, y, z

$$x=-1$$

$$y=-5$$

$$z=-5$$

Short Steps Using Substitution

Reorder the equations.

$$x-4y-6z=49 2x-46y=228 -4x-3y+4z=-1$$

Solve x-4y-6z=49 for x.

$$x=4y+6z+49$$

Substitute 4y+6z+49 for x in the second and third equation.

$$2\left(4y+6z+49\right)-46y=228 -4\left(4y+6z+49\right)-3y+4z=-1$$

Solve these equations for y and z respectively.

$$y=-\frac{65}{19}+\frac{6}{19}z z=-\frac{19}{20}y-\frac{39}{4}$$

Substitute -\frac{65}{19}+\frac{6}{19}z for y in the equation z=-\frac{19}{20}y-\frac{39}{4}.

$$z=-\frac{19}{20}\left(-\frac{65}{19}+\frac{6}{19}z\right)-\frac{39}{4}$$

Solve z=-\frac{19}{20}\left(-\frac{65}{19}+\frac{6}{19}z\right)-\frac{39}{4} for z.

$$z=-5$$

Substitute -5 for z in the equation y=-\frac{65}{19}+\frac{6}{19}z.

$$y=-\frac{65}{19}+\frac{6}{19}\left(-5\right)$$

Calculate y from y=-\frac{65}{19}+\frac{6}{19}\left(-5\right).

$$y=-5$$

Substitute -5 for y and -5 for z in the equation x=4y+6z+49.

$$x=4\left(-5\right)+6\left(-5\right)+49$$

Calculate x from x=4\left(-5\right)+6\left(-5\right)+49.

$$x=-1$$

The system is now solved.

$$x=-1 y=-5 z=-5$$