Solve {l}{4x+3y+3z=350}{4x+2y+5z=360}{8x+8y+10z=840}

$$\left\{ \begin{array} { l } { 4 x + 3 y + 3 z = 350 } \\ { 4 x + 2 y + 5 z = 360 } \\ { 8 x + 8 y + 10 z = 840 } \end{array} \right.$$

Solve for x, y, z

$$x=50$$

$$y=30$$

$$z=20$$

Short Steps Using Substitution

Solve 4x+3y+3z=350 for x.

$$x=-\frac{3}{4}y-\frac{3}{4}z+\frac{175}{2}$$

Substitute -\frac{3}{4}y-\frac{3}{4}z+\frac{175}{2} for x in the second and third equation.

$$4\left(-\frac{3}{4}y-\frac{3}{4}z+\frac{175}{2}\right)+2y+5z=360 8\left(-\frac{3}{4}y-\frac{3}{4}z+\frac{175}{2}\right)+8y+10z=840$$

Solve these equations for y and z respectively.

$$y=-10+2z z=35-\frac{1}{2}y$$

Substitute -10+2z for y in the equation z=35-\frac{1}{2}y.

$$z=35-\frac{1}{2}\left(-10+2z\right)$$

Solve z=35-\frac{1}{2}\left(-10+2z\right) for z.

$$z=20$$

Substitute 20 for z in the equation y=-10+2z.

$$y=-10+2\times 20$$

Calculate y from y=-10+2\times 20.

$$y=30$$

Substitute 30 for y and 20 for z in the equation x=-\frac{3}{4}y-\frac{3}{4}z+\frac{175}{2}.

$$x=-\frac{3}{4}\times 30-\frac{3}{4}\times 20+\frac{175}{2}$$

Calculate x from x=-\frac{3}{4}\times 30-\frac{3}{4}\times 20+\frac{175}{2}.

$$x=50$$

The system is now solved.

$$x=50 y=30 z=20$$