Solve {l}{3x-y=-7}{y+4z=3}{2x-2z=-5}

$$\left. \begin{array} { l } { 3 x - y = - 7 } \\ { y + 4 z = 3 } \\ { 2 x - 2 z = - 5 } \end{array} \right.$$

Solve for x, y, z

$$x=-2$$

$$y=1$$

$$z=\frac{1}{2}=0.5$$

Short Steps Using Substitution

Solve 3x-y=-7 for y.

$$y=3x+7$$

Substitute 3x+7 for y in the equation y+4z=3.

$$3x+7+4z=3$$

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

$$x=-\frac{4}{3}-\frac{4}{3}z z=x+\frac{5}{2}$$

Substitute -\frac{4}{3}-\frac{4}{3}z for x in the equation z=x+\frac{5}{2}.

$$z=-\frac{4}{3}-\frac{4}{3}z+\frac{5}{2}$$

Solve z=-\frac{4}{3}-\frac{4}{3}z+\frac{5}{2} for z.

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

Substitute \frac{1}{2} for z in the equation x=-\frac{4}{3}-\frac{4}{3}z.

$$x=-\frac{4}{3}-\frac{4}{3}\times \frac{1}{2}$$

Calculate x from x=-\frac{4}{3}-\frac{4}{3}\times \frac{1}{2}.

$$x=-2$$

Substitute -2 for x in the equation y=3x+7.

$$y=3\left(-2\right)+7$$

Calculate y from y=3\left(-2\right)+7.

$$y=1$$

The system is now solved.

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